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1. Satan, Cantor and Infinity: Mind-Boggling
2. Satan, Cantor and Infinity and
3. Set Theory and the Sizes of Infinity:
4. Infinity: Countable set, Cantor's
5. Transfinite number: Transfinite
6. Satan, Cantor & Infinity

1. Satan, Cantor and Infinity: Mind-Boggling Puzzles (Dover Books on Mathematical & Word Recreations)
by Raymond M. Smullyan
Paperback: 288 Pages (2009-03-26)
list price: US$12.95 -- used & new: US$7.84
(price subject to change: see help)
Asin: 0486470369
Average Customer Review: 5.0 out of 5 stars
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Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.
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Customer Reviews (1)

5-0 out of 5 stars A classic reprinted
I read this book many years ago as a checkout book from the library. Loved it! I was hoping for a long time that it would be reprinted. You will enjoy this Smullyan classic. ... Read more

2. Satan, Cantor and Infinity and Other Mind-boggling Puzzles
by Raymond M. Smullyan
 Paperback: 278 Pages (1993-02-18)

Isbn: 0192861611
Average Customer Review: 5.0 out of 5 stars
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A strange fate brings Princess Annabelle and her suitor Alexander to the Island of Knights and Knaves, where each inhabitant is either a Knight who always makes true statements, or a Knave who only makes false ones. They make friends with a sorcerer, who uses logic so cleverly that everyone thinks it is magic. Leading them through the complexities of logic, he takes them to a different island, where robots are programmed to make other robots with programmes of their own, and the reader has to work out what the programmes will be. The book ends with a guided tour of infinity, and we hear the remarkable story of how the devil was once outwitted by a student of the mathematician Georg Cantor. Raymond Smullyan is a mathematician and logician. He has also written "The Lady or the Tiger?", "Forever Undecided - a Puzzle Guide to Goedel", "To Mock a Mockingbird", "The Chess Mysteries of Sherlock Holmes" and "The Chess Mysteries of The Arabian Knights". ... Read more

Customer Reviews (6)

5-0 out of 5 stars To tell the truth...
Raymond Smullyan has been described (by Martin Gardner, no less) as the most entertaining logician ever (lets leave aside the lack of competition here -- after all, Kurt Godel wasn't known to be a bundle of laughs, etc. ...).One of the points of logic is to figure out what lines of reasoning make sense, and what can be considered true and false, given the proper rules of rational thought and the right information.

This can be done by means of equations, symbolic expressions and linguistic tools, but this can be rather dry.A much more enjoyable means of learning to apply logical principles is through the kinds of puzzles presented by Smullyan.It is somewhat ironic -- story problems are the point of greatest dread among many mathematics students, yet the logic-equivalent of story problems are the most fun!

Smullyan has written several books on logic puzzles, and often starts with the device of puzzles with figuring out who is telling the truth and who is lying -- here it starts on the island of Knights and Knaves, where Knights always tell the truth, and Knaves always tell lies.However, apart from this distinction, it is impossible to tell them apart.Smullyan presents the problems, and then presents the solutions, not in the back of the book or in a footnote, but as part of the narrative.It is a very natural and logical progression.

In this logic-puzzle-story, Smullyan introduces the Sorcerer, not really a magician, but someone so skilled in logical thought that he is considered a magical figure.He leads the path across the novel, including what Smullyan describes as a 'guided tour of infinity' -- it is here that Cantor (from the title, the mathematician George Cantor) is brought up.If you think all infinities are equal, guess again.If you think all mathematical infinities add up to the same, or have the same properties, you'd be wrong.But how can this be proved?

Smullyan ends the book with a story of one of Cantor's students outsmarting Satan, relying on language and set theory to confuse the naming of a set in a clever bargain.

The book is a wonderful romp through logic, set theory, and rational thinking.It is not a simple book -- there are a number of places where equations and symbol logic methods are used; having at least a basic knowledge of algebra and elementary logic will make this book much more fun and accessible.However, many of the puzzles rely on common sense kinds of logic.

It is quite fun.Don't be a knave; read this book.

5-0 out of 5 stars Perhaps Smullyan's best
A highly enjoyable book of mathematical puzzles and ideas. Overall I think this is the best of the books by Smullyan I have seen, as the narrative (hardly a story, but a narrative of discussions which introduce and explain ideas) is very readable. Smullyan uses this technique in several other books but often one gets a sense that there is only a little narrative to connect much hard stuff - here the maths is interwoven into the narrative in a way that makes it much easier to follow (for example, the characters make various comments and objections which the central character, the Sorcerer, responds to as if engaged in an informal tutorial).

5-0 out of 5 stars Satan, Cantor, and Infinity - a novel about set theory
Professor Smullyan's book Satan, Cantor, and Infinity, is an excellent mathematical novel, extremely readable for everybody from elementary schoolboys(girls)to first class college (university) students. The story concerns three major personalities - The Sorcerer living in the Knight-Knave Island and Princess Annabelle with her suitor. As in many books of professor Smullyan the first half of the story is devoted to various puzzles about knights (truth-tellers) and knaves (liars). The third chapter takes place on the island of robots. The puzzles of self-constructive and self-destructive robots throw light on problem of languages, which allow self-reference, and the famous Gödel's theorems. This chapter may be harder to catch and the reader is recommended to consult another professor Smullyan's book, Forever Undecided. In the rest of the book are introduced Zeno's paradoxes concerning the problem of continuity and change (with these paradoxes are discussed the most elementary ideas of infinitesimal calculus), envelope paradox (a kind of paradox of rationality), ant the set-theoretic paradoxes (Burry's paradox, Mannoury's paradox, Russell's paradox and Cantor's paradox). The basic ideas of set theory are introduced in the form of problems of a prisoner in the Hell - Satan gives the prisoner opportunity to save himself(herself) if he(she) puzzles out an integer which Satan wrote on the paper closed in an envelope. Story also introduces the famous Continuum problem - the set theoretic problem formulated by the founder of set theory Georg Cantor in the 19th century and unsolved to our times (or at least unsolved by the more modest set theoretic principles not using some hypotheses concerning large cardinals). The story concludes with a nice Zwicker's hypergame paradox and a legend about a gifted student of Cantor imprisoned in Hell, who outwits the Great Satan. The entire book is written in non-technical style and really is a MATHEMATICAL NOVEL, maybe a mathematical fairy tale, not a textbook. (I would only like to know if professor Smullyan is really going to fulfill his promise given in the book that he will try to present more calculus ideas in the future.) Well, the book is very delightful reading for these days - the Good defeats the Evil even in this story, even in the realm of mathematics!

5-0 out of 5 stars The best logic puzzles you will find
Before you start reading this book, prepare to have your logic bone tweaked, tickled and annoyed. There is no one betterthan Raymond Smullyan at creating logic puzzles that will intrigue, infuriate and stretch your mind to slightly beyond its limits. The last chapter, a dialog between Satan and a student of Cantor, could be the basis of a book and is a true work of genius. I read it twice, not because I didn't understand it, but because I enjoyed it so much.
The other sections of the book cover many facets of logic, including lists of superb problems about people from the planet Og, where green northerners always tell the truth and red northerners always lie. However, green southerners always lie and red southerners always tell the truth. Similar to the knights and knaves problems, most can be solved using a simple table. Solutions to the problems are given at the end of each chapter.
Raymond Smullyan seems to exist at a different logical level than the rest of us. His problems are at times fiendishly clever, although not beyond the capacity of someone willing to think a bit. This is a case where you can expand your mind by showing how limited it was before.

5-0 out of 5 stars Extremely interesting if you love logic puzzles
This is a VERY good book some puzzles are easier and some harder, but all of them have an answer. hours of fun! when you are done go back and see if you can do some of the harder puzzles without peeking at the answer. ... Read more

3. Set Theory and the Sizes of Infinity: An entry from Gale's <i>Science and Its Times</i>
by Sherri Chasin Calvo
 Digital: 2 Pages (2000)
list price: US$4.90 -- used & new: US$4.90
(price subject to change: see help)
Asin: B0027UWT00
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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 1271 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

4. Infinity: Countable set, Cantor's diagonal argument, Surreal number, Continuum hypothesis, Hyperreal number, Extended real number line
Paperback: 190 Pages (2010-10-18)
list price: US$27.92 -- used & new: US$27.92
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Asin: 1157249906
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Chapters: Countable set, Cantor's diagonal argument, Surreal number, Continuum hypothesis, Hyperreal number, Extended real number line, Uncountable set, Where Mathematics Comes From, Absolute Infinite, Ultrafinitism, Infinitesimal, Infinite monkey theorem, Actual infinity, Non-standard calculus, Real projective line, Cardinality of the continuum, Temporal finitism, Aleph number, Beth number, Line at infinity, Plane at infinity, Point at infinity, Hyperplane at infinity, Infinity plus one, Superreal number, Hyperinteger, Circular points at infinity, Directed infinity,. Source: Wikipedia. Pages: 189. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. In a rigorous set theoretic sense, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed. The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first pres...http://booksllc.net/?id=51432 ... Read more

5. Transfinite number: Transfinite Number, Cardinal Number, Ordinal Number, Finite Set, Absolute Infinite, Georg Cantor, Infinity, Cardinality
Paperback: 92 Pages (2010-02-03)
list price: US$47.00
Isbn: 6130353987
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High Quality Content by WIKIPEDIA articles! Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use. ... Read more

6. Satan, Cantor & Infinity
by Raymond M. Smullyan
 Hardcover: Pages (1994-06-12)
list price: US$4.99
Isbn: 0517118009
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