Insel der Zahlen

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 Conways 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 books primary aim Knuth explains in a postscript is not so much to teach Conways 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 Conways 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 how new mathematics is created. 0201038129B04062001