Nearly 30 years ago, John Horton Conway introduced a new way to
construct numbers. Donald E. Knuth, in appreciation of this
revolutionary system, took a week off from work on The Art of
Computer Programming to write an introduction to Conway's method.
Never content with the ordinary, Knuth wrote this introduction as a
work of fiction--a novelette. If not a steamy romance, the book
nonetheless shows how a young couple turned on to pure mathematics
and found total happiness.
The book's primary aim, Knuth explains in a postscript, is not
so much to teach Conway's theory as "to teach how one might go
about developing such a theory." He continues: "Therefore, as the
two characters in this book gradually explore and build up Conway's
number system, I have recorded their false starts and frustrations
as well as their good ideas. I wanted to give a reasonably faithful
portrayal of the important principles, techniques, joys, passions,
and philosophy of mathematics, so I wrote the story as I was
actually doing the research myself..,." It is an astonishing feat
of legerdemain. An empty hat rests on a table made of a few axioms
of standard set theory. Conway waves two simple rules in the air,
then reaches into almost nothing and pulls out an infinitely rich
tapestry of numbers that form a real and closed field. Every real
number is surrounded by a host of new numbers that lie closer to it
than any other "real" value does. The system is truly "surreal."
"quoted from Martin Gardner, Mathematical Magic Show, pp.
16--19"
Surreal Numbers, now in its 13th printing, will appeal to anyone
who might enjoy an engaging dialogue on abstract mathematical
ideas, and who might wish to experience hownew mathematics is
created.
0201038129B04062001
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