[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,
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
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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