id: 06418218
dt: b
an: 2015d.00514
au: Ovchinnikov, Sergei
ti: Number systems. An introduction to algebra and analysis.
so: Pure and Applied Undergraduate Texts 23. Providence, RI: American
Mathematical Society (AMS) (ISBN 978-1-4704-2018-5/hbk). viii, 144~p.
(2015).
py: 2015
pu: Providence, RI: American Mathematical Society (AMS)
la: EN
cc: F15
ut: natural number; real number; complex number; Dedekind completeness
properties
ci:
li:
ab: This book is intended to provide an introduction to the five basic number
systems of mathematics, namely natural numbers, integers, rational
numbers, real numbers, and complex numbers. After a presentation of the
Peano theory, the author is concerned with some basic methods like
mathematical induction and recursion theory. Next, there are given the
properties of integer numbers, rings and ordered integral domains. The
presentation of rational numbers includes material on ordered fields
and convergence of sequences in these fields. Cauchy and Dedekind
completeness properties of the field of real numbers play a central
role in this volume. A key feature of this book is an elementary proof
of the fundamental theorem of algebra, which is given in relationship
with the properties of complex numbers. Useful problems are given at
the end of any of the five chapters of this volume. As a conclusion,
this is a nicely written book to share with colleagues and students, a
wonderful addition to our personal, school and university libraries.
rv: Teodora-Liliana RÄƒdulescu (Craiova)