Basic Set Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Basic Set Theory PDF full book. Access full book title Basic Set Theory by Azriel Levy. Download full books in PDF and EPUB format.
Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418
Get Book
Book Description
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418
Get Book
Book Description
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
Author: Steve Warner
Publisher:
ISBN: 9780999811764
Category :
Languages : en
Pages :
Get Book
Book Description
Set Theory for BeginnersSet Theory for Beginners consists of a series of basic to intermediate lessons in set theory. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in set theory high school teachers working with advanced math students students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and mathematical logic. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Set Theory Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets Lesson 2 - Subsets Lesson 3 - Operations on Sets Lesson 4 - Relations Lesson 5 - Equivalence Relations and Partitions Lesson 6 - Functions Lesson 7 - Equinumerosity Lesson 8 - Induction and Recursion on N Lesson 9 - Propositional Logic Lesson 10 - First-order Logic Lesson 11 - Axiomatic Set Theory Lesson 12 - Ordinals Lesson 13 - Cardinals Lesson 14 - Martin's Axiom Lesson 15 - The Field of Real Numbers Lesson 16 - Clubs and Stationary Sets
Author: Joseph Breuer
Publisher: Courier Corporation
ISBN: 0486154874
Category : Mathematics
Languages : en
Pages : 130
Get Book
Book Description
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author: Winfried Just
Publisher: American Mathematical Soc.
ISBN: 0821802666
Category : Mathematics
Languages : en
Pages : 210
Get Book
Book Description
This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
Author: Herbert B. Enderton
Publisher: Academic Press
ISBN: 0080570429
Category : Mathematics
Languages : en
Pages : 279
Get Book
Book Description
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category : Mathematics
Languages : en
Pages : 259
Get Book
Book Description
"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: D.C. Goldrei
Publisher: Routledge
ISBN: 1351460617
Category : Mathematics
Languages : en
Pages : 296
Get Book
Book Description
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: Steve Warner
Publisher:
ISBN: 9781951619022
Category : Mathematics
Languages : en
Pages : 106
Get Book
Book Description
Set Theory for Beginners - Solution GuideThis book contains complete solutions to the problems in the 16 Problem Sets in Set Theory for Beginners. Note that this book references examples and theorems from Set Theory for Beginners. Therefore, it is strongly suggested that you purchase a copy of that book before purchasing this one.
Author: Richard Kohar
Publisher: World Scientific Publishing Company
ISBN: 9814730416
Category : Mathematics
Languages : en
Pages : 732
Get Book
Book Description
This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. "Written with clarity, humor and relevant real-world examples, Basic Discrete Mathematics is a wonderful introduction to discrete mathematical reasoning."- Arthur Benjamin, Professor of Mathematics at Harvey Mudd College, and author of The Magic of Math
Author: Abhijit Dasgupta
Publisher: Springer Science & Business Media
ISBN: 1461488540
Category : Mathematics
Languages : en
Pages : 434
Get Book
Book Description
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.
