An Editor Recalls Some Hopeless Papers

1998 ◽  
Vol 4 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Wilfrid Hodges
Keyword(s):  
Natural Numbers ◽  
Real Numbers ◽  
Diagonal Argument ◽  
The One ◽  
Academy Of Sciences ◽  
Main Message

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument (I mean the one proving that the set of real numbers and the set of natural numbers have different cardinalities) have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank ([9] pp. 44f, 354).

scholarly journals The Diagonalization Paradox

2020 ◽  
Author(s):  
Ron Ragusa
Keyword(s):  
Initial Conditions ◽  
Open Interval ◽  
Georg Cantor ◽  
Natural Numbers ◽  
Real Numbers ◽  
The Real ◽  
Diagonal Argument ◽  
One To One

In 1891 Georg Cantor published his Diagonal Argument which, he asserted, proved that the real numbers cannot be put into a one-to-one correspondence with the natural numbers. In this paper we will see how by varying the initial conditions of the demonstration we can use Cantor’s method to produce a one-to-one correspondence between the set of natural numbers and the set of infinite binary decimals in the open interval (0, 1).

scholarly journals The way to list all infinite real numbers and to construct a bijection between natural numbers and real numbers

2021 ◽  
Author(s):  
Shee-Ping Chen
Keyword(s):  
Georg Cantor ◽  
Natural Numbers ◽  
Real Numbers ◽  
Diagonal Argument ◽  
Infinite Sets ◽  
The Way

Abstract Georg Cantor defined countable and uncountable sets for infinite sets. The set of natural numbers is defined as a countable set, and the set of real numbers is proved to be uncountable by Cantor’s diagonal argument. Most scholars accept that it is impossible to construct a bijection between the set of natural numbers and the set of real numbers. However, the way to construct a bijection between the set of natural numbers and the set of real numbers is proposed in this paper. The set of real numbers can be proved to be countable by Cantor’s definition. Cantor’s diagonal argument is challenged because it also can prove the set of natural numbers to be uncountable. The process of argumentation provides us new perspectives to consider about the size of infinite sets.

scholarly journals The Diagonalization Paradox - Expanded

2020 ◽  
Author(s):  
Ron Ragusa
Keyword(s):  
Initial Conditions ◽  
Georg Cantor ◽  
Natural Numbers ◽  
Real Numbers ◽  
The Real ◽  
One To One ◽  
The One

In 1891 Georg Cantor published his Diagonal Method which, he asserted, proved that the real numbers cannot be put into a one-to-one correspondence with the natural numbers. In this paper we will see how by varying the initial conditions of Cantor’s proof we can use the diagonal method to produce a one-to-one correspondence between the set of natural numbers and the set of infinite binary decimals in the interval (0, 1). In the appendix we demonstrate that using the diagonal method recursively will, at the limit of the process, fully account for all the infinite binary decimals in (0, 1). The proof will cement the one-to-one correspondence between the natural numbers and the infinite binary decimals in (0, 1).

Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

2021 ◽  
pp. 1-11
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev
Keyword(s):  
Comparative Analysis ◽  
Real Data ◽  
Intuitionistic Fuzzy Sets ◽  
Real Numbers ◽  
Data Set ◽  
Important Method ◽  
Ticket Sales ◽  
Intuitionistic Fuzzy ◽  
The One ◽  
First Time

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

scholarly journals The New Evolution for SIA Rotorcraft UAV Project

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Juntong Qi ◽  
Dalei Song ◽  
Lei Dai ◽  
Jianda Han ◽  
Yuechao Wang
Keyword(s):  
Control Method ◽  
Test Bed ◽  
Advanced Control ◽  
Autonomous Mode ◽  
Chinese Academy Of Sciences ◽  
Aerial Vehicle ◽  
Active Modeling ◽  
Rotorcraft Uav ◽  
The One ◽  
Academy Of Sciences

This paper describes recent research on the design, implement, and testing of a new small-scaled rotorcraft Unmanned Aerial Vehicle (RUAV) system—ServoHeli-40. A turbine-powered UAV weighted less than 15 kg was designed, and its major components were tested at the Shenyang Institute of Automation, Chinese Academy of Sciences in Shenyang, China. The aircraft was designed to reach a top speed of more than 20 mps, flying a distance of more than 10 kilometers, and it is going to be used as a test-bed for experimentally evaluating advanced control methodologies dedicated on improving the maneuverability, reliability, as well as autonomy of RUAV. Sensors and controller are all onboard. The full system has been tested successfully in the autonomous mode using the multichannel active modeling controller. The results show that in a real windy environment the rotorcraft UAV can follow the trajectory which was assigned by the ground control station exactly, and the new control method is obviously more effective than the one in the past year's research.

Mathematical Knowledge and the Origin of Phenomenology

2021 ◽  
Vol 21 ◽  
pp. 273-294
Author(s):  
Gabriele Baratelli ◽  
Keyword(s):  
Mathematical Knowledge ◽  
Cardinal Number ◽  
The Other ◽  
Mathematical Science ◽  
Natural Numbers ◽  
Symbolic Thinking ◽  
The One

The paper is divided into two parts. In the first one, I set forth a hypothesis to explain the failure of Husserl’s project presented in the Philosophie der Arithmetik based on the principle that the entire mathematical science is grounded in the concept of cardinal number. It is argued that Husserl’s analysis of the nature of the symbols used in the decadal system forces the rejection of this principle. In the second part, I take into account Husserl’s explanation of why, albeit independent of natural numbers, the system is nonetheless correct. It is shown that its justification involves, on the one hand, a new conception of symbols and symbolic thinking, and on the other, the recognition of the question of “the formal” and formalization as pivotal to understand “the mathematical” overall.

Buddhist art in the museum as a source base of scientific research

2019 ◽  
Author(s):  
Светлана Гарриевна Батырева
Keyword(s):  
Art Criticism ◽  
Traditional Culture ◽  
Museum Collection ◽  
Buddhist Art ◽  
Scientific Center ◽  
Research Activities ◽  
The People ◽  
Initial Work ◽  
The One ◽  
Academy Of Sciences

В настоящей статье рассматривается проблема изучения музейной коллекции буддийского изобразительного искусства Калмыкии, а также сохранения художественного наследия в условиях глобализации культур. Автор ставит цель создать научно обоснованные информационные ресурсы на базе исследования музейных коллекций и экспонатов. Информация составляет суть музейного дела, в основе которого лежит научно-исследовательская деятельность, объединяющая сферы комплектования, учета и хранения фондов, с одной стороны, с другой коммуникативная, связанная с экспозиционно-выставочной деятельностью. Исходными в работе музея являются не только сохраняемый фонд, но и сведения об экспонатах, собираемые в процессе комплектования фонда и создания каталога музейного собрания, состоящего из коллекций. Основываясь на богатой традиции описания и каталогизации предметов искусства, а также применяя современные технологии и искусствоведческие методы, стало возможным подготовить и издать научный каталог коллекций основного фонда Музея традиционной культуры имени Зая-пандиты Калмыцкого научного центра РАН. This article discusses the problem of studying the museum collection of Buddhist fine art in Kalmykia, as well as preserving the artistic heritage in the context of globalization of cultures. The author aims to create scientifically based information resources that include research on museum collections and exhibits. Information is the essence of museum business, which is based on research activities that combine the fields of acquisition, accounting and storage of funds, on the one hand, and on the other hand, communicative activities related to exposition and exhibition activities. The initial work of the museum is not only the preserved fund, but also information about the exhibits collected in the process of acquiring the fund and creating a museum collection catalog consisting of collections. The Zaya-Pandita Museum of Traditional Culture of the Kalmyk Scientific Center of the Russian Academy of Sciences stores and presents in the educational sphere multidisciplinary and largely unique information about the cultural heritage of the people. Based on a rich tradition of describing and cataloging objects of art, as well as using modern technologies and art criticism methods, it has become possible to prepare and publish a scientific catalog of the collections of the main fund of the Zaya-Pandita Museum of Traditional Culture.

scholarly journals Intra-firm mobility of scientific staff of the Russian Academy of Sciences

POPULATION ◽  
2019 ◽  
Vol 22 (2) ◽  
pp. 105-119
Author(s):  
Olga Kolennikova
Keyword(s):  
Professional Growth ◽  
Large Scale ◽  
Labor Mobility ◽  
Top Management ◽  
Russian Academy Of Sciences ◽  
Scientific Staff ◽  
Career Growth ◽  
The One ◽  
Academy Of Sciences ◽  
Scientific Environment

The article is devoted to the study of intra-firm labor mobility and the opportunities for updating the composition of research personnel, including managers. The information base was the data from the questionnaire survey of the personnel of the institutes of the Russian Academy of Sciences, carried out by the Institute of Socio-Economic Studies of Population RAS in 2015. The age limit set for heads of institutions, the established standards for young research fellows and other measures have changed the mechanism of labor mobility. Changes in the position of researchers of different categories have been analyzed with the account of the factors facilitating career growth or, on the contrary, complicating it. It turned out that junior researchers and top-management were the most mobile categories in the personnel hierarchy. The summary picture of the career advancement to top management, on the one hand, showed its availability for employees with different starting opportunities, and on the other hand, provided insight into the personnel reserves of candidates for the position of director and deputy director for research. Career attitudes were correlated with the assessment of the reality of their implementation. The process of accelerated rejuvenation of the RAS personnel can be described as controversial, especially in connection with the large-scale changes in the top management. The internal potential of candidates for director’s post was also investigated. According to the study, it is not high enough, and the chances of a person from the outside are significant. It looks like normalization of the intra-firm mobility of researchers, including rotation of managerial personnel, is possible not so much by administrative regulation, as through the all-round development of the scientific environment in which there is a qualitative professional growth of scientific personnel.

Proceed with care, because some infinities are larger than others

2020 ◽  
pp. 281-292
Author(s):  
Susan D'Agostino
Keyword(s):  
Number Line ◽  
Mathematics Students ◽  
Natural Numbers ◽  
Real Numbers ◽  
Countable Infinity ◽  
One To One ◽  
Infinite Set

“Proceed with care, because some infinities are larger than others” explains in detail why the infinite set of real numbers—all of the numbers on the number line—represents a far larger infinity than the infinite set of natural numbers—the counting numbers. Readers learn to distinguish between countable infinity and uncountable infinity by way of a method known as a “one-to-one correspondence.” Mathematics students and enthusiasts are encouraged to proceed with care in both mathematics and life, lest they confuse countable infinity with uncountable infinity, large with unfathomably large, or order with disorder. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

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