
- 112 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Naive Set Theory
About this book
This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.
"This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics." — Allen Stenger, The Mathematical Association of America, September 2011.
"This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics." — Allen Stenger, The Mathematical Association of America, September 2011.
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Yes, you can access Naive Set Theory by Paul R. Halmos in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Title Page
- Copyright Page
- Preface
- Contents
- Section 1: The Axiom of Extension
- Section 2: The Axiom of Specification
- Section 3: Unordered Pairs
- Section 4: Unions and Intersections
- Section 5: Complements and Powers
- Section 6: Ordered Pairs
- Section 7: Relations
- Section 8: Functions
- Section 9: Families
- Section 10: Inverses and Composites
- Section 11: Numbers
- Section 12: The Peano Axioms
- Section 13: Arithmetic
- Section 14: Order
- Section 15: The Axiom of Choice
- Section 16: Zorn’s Lemma
- Section 17: Well Ordering
- Section 18: Transfinite Recursion
- Section 19: Ordinal Numbers
- Section 20: Sets of Ordinal Numbers
- Section 21: Ordinal Arithmetic
- Section 22: The Schroder-Bernstein Theorem
- Section 23: Countable Sets
- Section 24: Cardinal Arithmetic
- Section 25: Cardinal Numbers
- Index