Surreal Numbers

Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.

出版者:Addison Wesley

作者:[美] Donald Knuth

页数:119

出版时间:1974-1-1

价格:GBP 18.99

装帧:Paperback

isbn号码:9780201038125

图书标签:数学计算机科学MathKnuth小说计算机SurrealNumber

From the Back Cover

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 how new mathematics is created.

读后感

确实是好东西，很值得一看，个人认为出彩的部分是译者对作者意思的精准把握，确实是传神之作。 第 25 页“如果成立的话，那我就会将 (Y, phi) （此处 phi 表示空集）称为“正”数”，之后又发现此中 Y 必须满足其中至少一个元素大于或相似于 0，只要满足了这个条件，它就成被称...  

《研究之美》这本书，讲述了一对情侣一次偶然地遇到了一些记有各种不认识的符号的石头，并通过研究这些符号之间的关系，从而发现了一种新理论的故事。这种理论，从书的前言可以知道，称为 Conway 的超实数理论。 此书是斯坦福大学的非常有名的高德纳教授所写。在大二时候，我...  

我看这里的留言，包括书评和笔记没一个人说明白这本书到底讲了个什么，到底什么思路，整体脉络到底是什么的问题，总在扯些没用的，所以我决定留言在这里。 这本书是这样，英文名应该叫 超现实的数，其实就是说一种数论吧，原文是这样写的 他们两个发现石碑后，觉得这应该是一...  

《研究之美》这本书，讲述了一对情侣一次偶然地遇到了一些记有各种不认识的符号的石头，并通过研究这些符号之间的关系，从而发现了一种新理论的故事。这种理论，从书的前言可以知道，称为 Conway 的超实数理论。 此书是斯坦福大学的非常有名的高德纳教授所写。在大二时候，我...  

用户评价

对话体形式来讨论自然数这个基础，在此基础上定义了加法和乘法，非常的严谨，不过也很抽象比较难以理解，对人的挑战很大！

数学证明看得好累，没看出他跟计算机科学的关系，研究之美这思想还是不错的

http://en.wikipedia.org/wiki/Surreal_number

虽然是大神写的。。。可是读了一半就读不下去了。不是很喜欢这种风格。。。

读起来不轻松。。。不过能和一个人擦出思想的火花一定是很美妙的一件事:) "There are infinitely many things yet to do...and only a finite amount of time..."