A new look at infinitely large and infinitely small quantities: Methodological foundations and practical calculations with these numbers on a computer

2021 ◽  
pp. 5-22
Author(s):  
Ya. D. Sergeyev
Keyword(s):  
Great Britain ◽  
Mathematical Knowledge ◽  
Computational Tools ◽  
Mathematical Objects ◽  
Modern Physics ◽  
Numeral Systems ◽  
Infinite Sets ◽  
Infinity Computer ◽  
The Way ◽  
New Look

This article describes a recently proposed methodology that allows one to work with infinitely large and infinitely small quantities on a computer. The approach uses a number of ideas that bring it closer to modern physics, in particular, the relativity of mathematical knowledge and its dependence on the tools used by mathematicians in their studies are discussed. It is shown that the emergence of new computational tools influences the way we perceive traditional mathematical objects, and also helps to discover new interesting objects and problems. It is discussed that many difficulties and paradoxes regarding infinity do not depend on its nature, but are the result of the weakness of the traditional numeral systems used to work with infinitely large and infinitely small quantities. A numeral system is proposed that not only allows one to work with these quantities analytically in a simpler and more intuitive way, but also makes possible practical calculations on the Infinity Computer, patented in a number of countries. Examples of measuring infinite sets with the accuracy of one element are given and it is shown that the new methodology avoids the appearance of some well-known paradoxes associated with infinity. Examples of solving a number of computational problems are given and some results of teaching the described methodology in Italy and Great Britain are discussed.

A New Look at Child Health

PEDIATRICS ◽  
1967 ◽  
Vol 39 (4) ◽  
pp. 636-636
Author(s):  
THOMAS E. CONE
Keyword(s):  
United States ◽  
Great Britain ◽  
Medical Students ◽  
Child Health ◽  
The United States ◽  
The State ◽  
Changing Patterns ◽  
New Look

This little paperback book is a gem which may escape the attention of readers on this side of the Atlantic because it deals mainly with the state of contemporary pediatrics in Great Britain. For us not to be aware of this book would be a mistake; many of the problems and shortcomings which Drs. Joseph and MacKeith discuss are equally germane to the United States. The authors attempt to define in 11 chapters such elusive things as just what pediatrics really is, what are the crucial current problems, how the changing patterns of death and morbidity in childhood have altered the demands on pediatricians, and—throughout the book as a leitmotiv—how to make medical students and physicians more aware of preventive aspects of medicine.

1.—The Competitors and the Result

1906 ◽  
Vol 10 (40) ◽  
pp. 50-51
Keyword(s):  
Great Britain ◽  
North Sea ◽  
English Channel ◽  
Long Distance ◽  
The North ◽  
The North Sea ◽  
The Way

No fewer than seven nations tried to win the Gordon Bennett Cup in the race which started from the Tuileries Gardens, in Paris, on September 30th. But the wind was in an unfavourable direction for the accomplishment of a long distance record. To some, the English Channel barred the way, to some, the North Sea.The cup offered for the greatest distance covered has been accorded to the American aeronaut, Mr. Frank P. Lahm, who descended 15 miles north of Scarborough.It will be seen in another part of this Journal that in December next, Members of the Aëronautical Society of Great Britain will hear an account of the Gordon-Bennett race from Colonel J. E. Capper, who took part in the race, having accompanied Mr. Rolls in the “ Britannia.” In this account, therefore, it will suffice to merely tabulate the competitors and results.

scholarly journals Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge

2020 ◽  
pp. 58-86
Author(s):  
Semjon F. Adlaj ◽  
◽  
Sergey N. Pozdniakov ◽  
Keyword(s):  
Comparative Analysis ◽  
Digital Media ◽  
Mathematical Knowledge ◽  
Information Environment ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Computer Tools ◽  
Digital Representations ◽  
The Impact

This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.

Freedom All the Way Up: A New Look

2021 ◽  
pp. 1-12
Author(s):  
Joseph A. Bracken
Keyword(s):  
The Way ◽  
New Look

Brief notes on Unemployment Insurance in Great Britain

1937 ◽  
Vol 5 (01) ◽  
pp. 4-14
Author(s):  
F. J. C. Honey
Keyword(s):  
Great Britain ◽  
Unemployment Insurance ◽  
Full Information ◽  
Comprehensive Review ◽  
National Insurance ◽  
Original Scheme ◽  
The Way

It is impossible in these notes to attempt any comprehensive review of the system of compulsory Unemployment Insurance which has operated in this country since 1912. Moreover, the paper by Messrs Kyd & Maddex read before the Institute in January 1929 gives full information up to that date. But I want to start by outlining the original scheme, as I think the way in which it has been modified and extended may be found of interest.The system began with the National Insurance Act, 1911, Part II. Contributions commenced in July 1912 and benefit in January 1913. Only a few industries which were considered to carry a specially heavy risk of unemployment were included, and the numbers insured at the outset were about 2¼ millions. Contributions were 2¼d. per week each from employer and worker, and 1⅔d. from the Exchequer. Benefit was 7s. per week, with a limitation of one week's benefit for every five contributions paid, and a maximum of fifteen weeks' benefit in a year.

Mathematical texts

2020 ◽  
pp. 1032-1040
Author(s):  
Annette Imhausen
Keyword(s):  
Mathematical Knowledge ◽  
Primary Source ◽  
Ancient Egypt ◽  
Source Material ◽  
Ancient Egyptian ◽  
Modern Analysis ◽  
Mathematical Techniques ◽  
Mathematical Texts ◽  
The Way

Approximately a dozen mathematical papyri have survived from ancient Egypt. Based on their script (but also their stage of the Egyptian language) they fall into two groups—hieratic and demotic texts. These papyri constitute our primary source material to learn about ancient Egyptian mathematics. Because of the procedural style that they were written in, it is assumed that they were used in teaching junior scribes the mathematical techniques they would need for their job; however, the procedural format may also have constituted the way of collecting mathematical knowledge at the time. It is only if this format is taken into account in the (modern) analysis of Egyptian mathematical texts that their sophistication becomes visible, and a deeper understanding of Egyptian mathematics beyond rudimentary similarities to modern equivalents can therefore be achieved.

New look Bulletin on the way

1998 ◽  
Vol 23 (3) ◽  
pp. 193-194
Author(s):  
Judy Buttriss
Keyword(s):  
The Way ◽  
New Look
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