TY  - BOOK
AU  - Faticoni,Theodore G.
ED  - Wiley InterScience (Online service)
TI  - The mathematics of infinity: a guide to great ideas 
T2  - Pure and applied mathematics
SN  - 9781118243879
AV  - QA248 .F29 2012
U1  - 511.3/22 23
PY  - 2012///
CY  - Hoboken, N.J.
PB  - John Wiley & Sons
KW  - Cardinal numbers
KW  - Set theory
KW  - Infinite
KW  - MATHEMATICS
KW  - Infinity
KW  - Mathematics
KW  - bisacsh
KW  - fast
KW  - Mengenlehre
KW  - gnd
KW  - Unendlichkeit
KW  - Kardinalzahl
KW  - local
KW  - Electronic books
N1  - Includes bibliographical references and index; Front Matter -- Logic -- Sets -- Functions -- Counting Infinite Sets -- Infinite Cardinals -- Well-Ordered Sets -- Inductions and Numbers -- Prime Numbers -- Logic and Meta-Mathematics -- Bibliography -- Index -- Wiley Series in Probability and Statistics --; 1. Logic -- 2. Sets -- 3. Functions -- 4. Counting infinite sets -- 5. Infinite cardinals -- 6. Well-ordered sets -- 7. Inductions and numbers -- 8. Prime numbers -- 9. Logic and meta-mathematics
N2  - "Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well ordered sets; inductions and numbers; prime numbers; and logic and meta-mathematics."--
UR  - http://onlinelibrary.wiley.com/book/10.1002/9781118243879
ER  -