[PDF] Classical Set Theory eBook

Author : Peter Komjath
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 21,99 MB
Release : 2006-11-22
Category : Mathematics
ISBN : 0387362193

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This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Author : D.C. Goldrei
Publisher : Routledge
Page : 300 pages
File Size : 19,10 MB
Release : 2017-09-06
Category : Mathematics
ISBN : 1351460609

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Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Author : Alexander Kechris
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 33,30 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461241901

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Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Author : Ernest Czogala
Publisher : Physica
Page : 207 pages
File Size : 49,37 MB
Release : 2012-08-10
Category : Computers
ISBN : 3790818534

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Intelligence systems. We perfonn routine tasks on a daily basis, as for example: • recognition of faces of persons (also faces not seen for many years), • identification of dangerous situations during car driving, • deciding to buy or sell stock, • reading hand-written symbols, • discriminating between vines made from Sauvignon Blanc, Syrah or Merlot grapes, and others. Human experts carry out the following: • diagnosing diseases, • localizing faults in electronic circuits, • optimal moves in chess games. It is possible to design artificial systems to replace or "duplicate" the human expert. There are many possible definitions of intelligence systems. One of them is that: an intelligence system is a system able to make decisions that would be regarded as intelligent ifthey were observed in humans. Intelligence systems adapt themselves using some example situations (inputs of a system) and their correct decisions (system's output). The system after this learning phase can make decisions automatically for future situations. This system can also perfonn tasks difficult or impossible to do for humans, as for example: compression of signals and digital channel equalization.

Author : George J. Klir
Publisher :
Page : 264 pages
File Size : 24,78 MB
Release : 1997
Category : Computers
ISBN :

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Fuzzy Set Theory: Foundations and Applications serves as a simple introduction to basic elements of fuzzy set theory. The emphasis is on a conceptual rather than a theoretical presentation of the material. Fuzzy Set Theory also contains an overview of the corresponding elements of classical set theory - including basic ideas of classical relations - as well as an overview of classical logic. Because the inclusion of background material in these classical foundations provides a self-contained course of study, students from many different academic backgrounds will have access to this important new theory.

Author : Krassimir T. Atanassov
Publisher : Physica
Page : 336 pages
File Size : 12,47 MB
Release : 2013-03-20
Category : Mathematics
ISBN : 3790818704

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In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 47,44 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Author : Abhijit Dasgupta
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 38,20 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 1461488540

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What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 31,92 MB
Release : 2014-07-23
Category : Mathematics
ISBN : 0486497089

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"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 49,28 MB
Release : 2013-03-09
Category : Business & Economics
ISBN : 9401579490

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Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.