# RAYMOND SMULLYAN

# SATAN, CANTOR,

AND INFINITY

#### AND OTHER MIND BOGGLING PUZZLES

Few things have stirred the imagination as much as Infinity! It has all sorts of curious properties which at first seem paradoxical, but then turn out not to be. As such, it provides ideal material for a puzzle book.

As with my earlier puzzle books, this one starts out with new puzzles about truth-tellers and liars ("knights" and "knaves"), but I have added a remarkable character known as the Sorcerer, who is considered a magician by those around him, although he is really a logician who uses logic so cleverly that it seems like magic to those not in the know. After many exhibitions of his "logical sorcery," he escorts us through a host of unusual adventures, including a visit to an island where intelligent robots create other robots and endow them with enough intelligence to create other intelligent robots, who in turn create other intelligent robots, and so forth, ad infinitum. Then, after some special puzzles related to G6del's famous theorem and some curious paradoxes about probability, time, and change, the Sorcerer gives us a guided tour of Infinity, explaining the pioneering discoveries of the great mathematician Georg Cantor, who was the first to put the subject on a logically sound basis. The Sorcerer, in his typically humorous fashion, ends up with a delightful tale of how Satan himself is outwitted by a clever student of Cantor's.

On the serious side, it must be wondered at that the whole fascinating subject of Infinity is so little known to the general public! Why isn't it taught in high schools? It is no harder to understand than algebra or geometry, and it is so rewarding! The last few chapters of this book provide an inviting (and easy) introduction to the subject. Even a neophyte can understand the nature of Infinity, Cantor's amazing contribution, and an account of what may be the greatest mathematical problem of all time which remains unsolved to this very day!

A NOTE TO THE READER

The several parts of the book do not have to be read in the order in which they appear. Thus, the reader primarily interested in Infinity can read Parts VI and VII quite independently of the rest of the book. Parts III and IV likewise form a separate unit, and Parts 1, II, and V can each be read independently.

All that a reader starting with later chapters needs to know is that the principal characters are the Sorcerer and his two students, Annabelle and Alexander.

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