Problems and Theorems in Classical Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Problems and Theorems in Classical Set Theory write by Peter Komjath. This book was released on 2006-05-02. Problems and Theorems in Classical Set Theory available in PDF, EPUB and Kindle. 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.
Problems and Theorems in Classical Set Theory
Problems and Theorems in Classical Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Problems and Theorems in Classical Set Theory write by Peter Komjath. This book was released on 2006-11-22. Problems and Theorems in Classical Set Theory available in PDF, EPUB and Kindle. 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.
Classic Set Theory
Classic Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Classic Set Theory write by D.C. Goldrei. This book was released on 2017-09-06. Classic Set Theory available in PDF, EPUB and Kindle. 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.
Set Theory
Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Set Theory write by Abhijit Dasgupta. This book was released on 2013-12-11. Set Theory available in PDF, EPUB and Kindle. 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.
A Book of Set Theory
A Book of Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Book of Set Theory write by Charles C Pinter. This book was released on 2014-07-23. A Book of Set Theory available in PDF, EPUB and Kindle. "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"--
