General Mathematics

2206 Submissions

[6] viXra:2206.0147 [pdf] replaced on 2022-07-10 10:04:28

Similarity of a Ramanujan Formula for $pi$ with Plouffe's Formulae, and Use of This for Searching of Physical Background for Some Guessed Formula for the Elementary Physical Constants

Authors: Janko Kokosar
Comments: 12 Pages.

The paper is comprised of two parts. In the first part, it discusses the similarity between one of Ramanujan's formulae for $pi$ and Plouffe's formulae where he uses the Bernoulli numbers. This similarity is help for further determination either that the similarity is only accidental, or that we can derive the Ramanujan formula in this way. This is also help for setting up a calculation system where we would estimate the probabilities with which we can obtain guessed formulae for $pi$ that are very accurate and very simple. (We only consider formulae that are not the approximations of the exact formulae for $pi$.) In the second part, it discusses various guessed formulae for the fine structure constant and for the other physical constants, and how the above probability calculation would help estimate whether these formulae have a physical basis or are only accidental.
Category: General Mathematics

[5] viXra:2206.0135 [pdf] submitted on 2022-06-25 12:05:05

Null Algebra Extension 1

Authors: Robert S. Miller
Comments: 31 Pages.

Null Algebra is algebraic exploration of division by 0, the resolution of negative roots to real values and the inclusion of extra space and time directions this mathematical discipline requires to work. This extension to Null Algebra explores the application of Null Algebra precepts to radical containing expressions which result in the feedback value, referred to in traditional mathematics as the indeterminate value.
Category: General Mathematics

[4] viXra:2206.0096 [pdf] submitted on 2022-06-18 12:27:12

The Intuitive Root of Classical Logic, an Associated Decision Problem and the Middle Way

Authors: Abhishek Majhi
Comments: 4 Pages.

We revisit Boole's reasoning regarding the equation ``$x.x=x$'' that sowed the seeds of classical logic. We discuss how he considered both ``$0.0=0$'' and ``$0.0\neq 0$'' in the ``same process of reasoning''. This can either be seen as a contradiction, or it can be seen as a situation where Boole could not decide whether ``$0.0=0$'' is universally valid -- an elementary ``decision problem'' in the words of Hilbert and Ackermann. We conclude that Boole's reasoning, that included a choice of ignorance, was founded upon the middle way of the Buddha, later mastered by Nagarjuna. From the modern standpoint, the situation can be likened to Turing's halting problem which resulted from the use of automatic machines and the exclusion of choice machines.
Category: General Mathematics

[3] viXra:2206.0092 [pdf] submitted on 2022-06-18 14:19:38

Logical Reasoning Including Mathematical Reasoning: Practical Problems and Possible Solution

Authors: Bertrand Wong
Comments: 5 Pages.

Logical reasoning in any form is an important aspect of life; it is persuading or convincing others with logic through writing or speech, for example, scientists, politicians, businessmen, financiers, solicitors and many others do this. This paper points out the frequent inefficacy of logical presentations, arguments and debates per se in bringing about the correct and wonted outcomes. It describes the scenario of people frequently involved in fruitless arguments and debates, and shows why the application of logic, for example, in logical argument or debate, could not often achieve the desired outcomes, much of the time ending up with frustration, unhappiness, bad feelings and poor relationships. Scenarios from mathematics, which probably represents the most rigorous form of logical reasoning, and science are described as well. The paper also delves into the problems encountered in logical reasoning as well as some modes of reasoning. It would be difficult and might be impossible to reason with and convince someone with a closed mind-set, someone who has made up the mind not to be convinced, or even someone who is not intelligent enough to be convinced. The paper, which is published in an international mathematics journal, presents a resolution to this serious problem, which is important, as that would be conducive to peace and harmony.
Category: General Mathematics

[2] viXra:2206.0058 [pdf] submitted on 2022-06-12 04:29:07

Yes, Checking = Solving, Says Calculus 1 & 2

By applying differential and integral calculus, this paper covers the principles and procedures for producing the solution of a problem, given the procedure for checking the correctness of the solution of a problem, and vice versa. If one is able to check quickly and completely, the correctness of the solution of a problem, one should also be able to produce the solution of the problem by reversing the order of the steps of the checking process, while using opposite operations in each step. The above principles were applied to four examples from calculus as well as to an example from geometry. Even though in calculus, one normally uses differentiation to check the correctness of an integration result, one will differentiate a function first, and then integrate the derivative to obtain the original function. One will differentiate the trigonometric functions, tan x, cot x, sec x and csc x; followed by integrating each derivative to obtain each original function. The results show that the solution process and the checking process are inverses of each other. In checking the correctness of the solution of a problem, one should produce the complete checking procedure which includes the beginning, the middle, and the end of the problem. Checking only the correctness of the final answer or statement is incomplete checking. To facilitate complete checking, the question should always be posed such that one is compelled to show a complete checking procedure from which the solution procedure can be produced. A general application of “Checking equals Solving” is that, if the correctness of the solution of a problem can be checked quickly and it is difficult to write a solution procedure, then first, one can write a complete checking procedure and reverse the order of the steps of the checking procedure while using opposite operations in each step, to obtain the solution procedure for the problem. Therefore, Checking equals Solving. Furthermore, every problem with a complete procedure for checking the correctness of the solution of the problem can be solved reasonably quickly.
Category: General Mathematics

[1] viXra:2206.0028 [pdf] submitted on 2022-06-06 14:52:11

Generalizing The Mean

Authors: Bharath Krishnan
Comments: 10 Pages.

I want to find a constructive extension of the average from the Hausdorff Measure and Integral w.r.t to that measure as the averages (from Tim Bedford and Albert M. Fisher) given for fractals, such that it gives a unique, and satisfying average for nowhere continuous functions defined on non-fractal, measurable sets in the sense of Caratheodory without a gauge function.
Category: General Mathematics