These xl and xr are not just numbers, theyre sets of numbers. Not very much at present, except for some use in game theory. Surreal numbers how two exstudents turned on to pure mathematics and found total happiness by donald e. Nearly 30 years ago, john horton conway introduced a new way to construct numbers. I started looking around the internet for information about surreal numbers, but what i found was no more than brief overviews. How two exstudents turned on to pure mathematics and found total happiness, 1974, isbn 0201038129. At times, they go in the wrong direction, at times they revert, but gradually they discover more and. Donald knuth s surreal numbers is a small little book telling the story of two people discovering john horton conways surreal numbers. Surreal numbers were introduced in donald knuths fiction book surreal. The term surreal number was invented by donald knuth 2. And the first number was created from the void left set. Nevertheless, surreal numbers are worth studying for two reasons.
How two exstudents turned on to pure mathematics and found total happiness. Okay, ill use capital letters for sets of numbers and small letters for numbers. Donald knuth of tex and the art of computer programming fame in his novel surreal. I started looking around the internet for information about surreal numbers, but what i found was no more than brief overviews and sketchy introductions that left me with even more questions. Donald knuths surreal numbers is a small little book telling the story of two people discovering john horton conways surreal numbers. Conways construction was introduced in donald knuths 1974 book surreal numbers. A platform for combinatorial computing new york, acm press 1993.
In mathematics, the surreal number system is a totally ordered proper class containing the real. Well start by using conways methods to represent games, and then show how. They discover them little by little and through dialog create a mathematical proof for the number system. Knuth surreal numbers addisonwesley publishing company inc. 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.
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