[FOM] a new book: Arithmetic of Infinity

Yaroslav D. Sergeyev yaro at si.deis.unical.it
Wed May 26 04:28:13 EDT 2004

Dear members of the FOM:

Please, find below a brief information regarding my new book 

Sergeyev Ya.D., Arithmetic of infinity,
Edizioni Orizzonti Meridionali, 2003, 112 pp., ISBN 88-89064-01-3

I hope that the book will be interesting to you. 

Thank you very much in advance,

Sincerely yours,


Yaroslav D. Sergeyev,  Ph.D., D.Sc. 
Dipartimento di Elettronica, Informatica e Sistemistica
Università della Calabria, Via P. Bucci, Cubo 41-C
87036 Rende (CS), Italia
Professor (part-time contract)
University of Nizhni Novgorod, pr. Gagarina, 23,
603600 Nizhni Novgorod, Russia
e-mail:    yaro at si.deis.unical.it
fax:     (+39)-0984-494713


The  book presents a new type of arithmetic that allows us to execute 

arithmetical operations with infinite numbers in the same manner as we are 

used to do with finite ones. The problem of infinity is considered in a 

coherent way different from those proposed by Georg Cantor, Abraham Robinson, 

and John Conway. However, the new approach does not contradict Cantor, it 

complements his theory. The new viewpoint gives detailed answers to many 

questions and paradoxes regarding infinite and infinitesimal quantities. 

Particularly, simple applications of the new approach to limit theory, 

measure theory, and set theory are given. The book opens new interesting
 perspectives for the theory of computations too.


The book is mainly addressed to mathematicians, physicists, computer

scientists, and students. However, it is written in such a way that any 

person having a high school education and who is interested in the foundations
 of these sciences will be able to understand it easily.



The book has been presented as the opening talk at the congress “Infinity in 

Mathematics, Physics, and Philosophy”, Pisa, 26.03.2004, and at the 

universities of: Aberdeen, Bologna, Calabria, Cardiff, Nizhni Novgorod, Pisa, 

Rome “La Sapienza”, Salerno, and also at the Computing Centre of the Russian 

Academy of Sciences, Moscow and at the Institute for High Performance 

Computing and Network of the Italian National Research Council.


About the author

Yaroslav D. Sergeyev holds a Full Professorship reserved for distinguished 

scientists at the University of Calabria, Rende, Italy. He is also a 

part-time Professor at the N.I. Lobatchevsky State University, Nizhni Novgorod,
Russia. He was awarded his Ph.D. (1990) from the same University and his D.Sc. 
degree from the M.V. Lomonosov State University of Moscow (1996). His research 

interests include numerical analysis, parallel computations, and number 

theory. His list of publications contains more than one hundred items 

including three books (the first has been published by Nizhni Novgorod 

University Press, the second by Kluwer Academic Publishers) and numerous 

papers in prestigious international journals. Additional information about 

the book can be found using this page


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