Naive Set Theory (eBook)

Paul R. Halmos (Autor)

eBook Download: EPUB

2017
112 Seiten
Dover Publications (Verlag)
978-0-486-82115-3 (ISBN)

Infos

Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.

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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. "e;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."e; — Allen Stenger, The Mathematical Association of America, September 2011.

Autor

Hungarian-born Paul R. Halmos (1916–2006) is widely regarded as a top-notch expositor of mathematics. He taught at the University of Chicago and the University of Michigan as well as other universities and made significant contributions to several areas of mathematics including mathematical logic, probability theory, ergodic theory, and functional analysis.

Inhalt

Preface. 1: The Axiom of Extension. 2: The Axiom of Specification. 3: Unordered Pairs. 4: Unions and Intersections. 5: Complements and Powers. 6: Ordered Pairs. 7: Relations. 8: Functions. 9: Families. 10: Inverses and Composites. 11: Numbers. 12: The Peano Axioms. 13: Arithmetic. 14: Order. 15: The Axiom of Choice. 16: Zorn's Lemma. 17: Well Ordering. 18: Transfinite Recursion. 19: Ordinal Numbers. 20: Sets of Ordinal Numbers. 21: Ordinal Arithmetic. 22: The Schröder-Bernstein Theorem. 23: Countable Sets. 24: Cardinal Arithmetic. 25: Cardinal numbers. Index

Produkt-Details

• Erscheint lt. Verlag: 19.4.2017
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 150 x 150 mm
• Gewicht: 154 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Schlagworte: advanced mathematics • axiomatic books • Cardinal Arithmetic • Cardinal numbers • Countable Sets • formal mathematics • how set theory is used • Logic • mathematical studies • Mathematics • Non-fiction • ordered pairs • ordinal numbers • science and math, Set theory • set theory • The Axiom of Choice • The Peano Axioms • The Schroeder-Bernstein Theorem • Transfinite methods • Transfinite recursion • Zorn's lemma
• ISBN-10: 0-486-82115-3 / 0486821153
• ISBN-13: 978-0-486-82115-3 / 9780486821153