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Axiomatic Set Theory (Dover Books on Mathematics),New
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One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: 'Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?' Answering this question by means of the ZermeloFraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level.The opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required.For the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in Axiomatic Set Theory provides a very clear and welldeveloped approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.
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- Q: What are the dimensions of 'Axiomatic Set Theory'? A: The book measures five point four one inches in length, zero point five six inches in width, and eight point four four inches in height. It is a standard paperback format.
- Q: How many pages does 'Axiomatic Set Theory' have? A: This book contains two hundred eighty-eight pages. It provides a comprehensive exploration of axiomatic set theory.
- Q: Who is the author of 'Axiomatic Set Theory'? A: The author is Patrick Suppes. He is known for his significant contributions to the field of mathematics and logic.
- Q: What is the binding type of 'Axiomatic Set Theory'? A: The binding type is paperback. This makes it lightweight and portable for students.
- Q: What is the reading level for 'Axiomatic Set Theory'? A: This book is suitable for upper undergraduate and graduate-level students. It requires some mathematical sophistication for full comprehension.
- Q: Is 'Axiomatic Set Theory' suitable for beginners? A: No, it is not recommended for beginners. A prior understanding of mathematical concepts is beneficial.
- Q: How can I use 'Axiomatic Set Theory' effectively? A: You can use this book as a textbook for advanced mathematics courses. It is designed to aid in the understanding of set theory foundations.
- Q: Are there exercises in 'Axiomatic Set Theory'? A: Yes, the book includes exercises that supplement the text. These are designed to reinforce the concepts discussed.
- Q: Can I skip chapters in 'Axiomatic Set Theory'? A: Yes, chapter six can be omitted without loss of continuity. It covers rational and real numbers, which some readers may find complex.
- Q: How should I care for 'Axiomatic Set Theory'? A: Keep it in a dry place to avoid damage. Avoid exposing it to direct sunlight to preserve its condition.
- Q: Is 'Axiomatic Set Theory' safe for all readers? A: Yes, it is safe for readers interested in mathematics. There are no adult themes or inappropriate content.
- Q: What if my copy of 'Axiomatic Set Theory' arrives damaged? A: You should contact the seller for a return or exchange. Most sellers have policies in place for damaged items.
- Q: Is there a warranty for 'Axiomatic Set Theory'? A: Typically, there is no warranty for books. Check with the retailer for their specific policies.
- Q: How does 'Axiomatic Set Theory' compare to other math textbooks? A: It provides a focused approach to axiomatic set theory, unlike many textbooks that cover broader topics. It is beneficial for those specifically interested in set theory.
- Q: Is 'Axiomatic Set Theory' appropriate for self-study? A: Yes, it can be used for self-study. However, a foundational knowledge of logic and mathematics is recommended for better understanding.