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Classic Set Theory

2017-09-06 Mathematics
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Release : 2017-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis Classic Set Theory by : D.C. Goldrei

Download or read book Classic Set Theory written by D.C. Goldrei. This book was released on 2017-09-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Problems and Theorems in Classical Set Theory

2006-11-22 Mathematics
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Release : 2006-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 193/5 ( reviews)

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Book Synopsis Problems and Theorems in Classical Set Theory by : Peter Komjath

Download or read book Problems and Theorems in Classical Set Theory written by Peter Komjath. This book was released on 2006-11-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classical Descriptive Set Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 901/5 ( reviews)

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Book Synopsis Classical Descriptive Set Theory by : Alexander Kechris

Download or read book Classical Descriptive Set Theory written by Alexander Kechris. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Notes on Set Theory

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 537/5 ( reviews)

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Book Synopsis Notes on Set Theory by : Yiannis Moschovakis

Download or read book Notes on Set Theory written by Yiannis Moschovakis. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

Introduction to Set Theory

1984 Mathematics
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Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to Set Theory by : Karel Hrbacek

Download or read book Introduction to Set Theory written by Karel Hrbacek. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt:

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