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Computing in a Surreal Realm

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Author:Ivars Peterson (MathLand)
Description: Even among mathematicians, the study of surreal numbers is an obscure pastime. Only a few have occupied themselves in recent years exploring the peculiarities of a number system that includes different kinds of infinities and vanishingly small quantities. The notion of surreal numbers goes back several decades. John H. Conway, then at Cambridge University, was trying to understand how to play Go, an immensely challenging board game popular in China and Japan. Careful study convinced him that the game could be interpreted as the sum of a large number of smaller, simpler games. Conway applied the same logic to other games of strategy, including checkers and dominoes, and he came to the conclusion that certain types of games appear to behave like numbers with distinctive properties. Conway's surreal numbers incorporate the idea that there exist different sizes of infinity, a notion investigated more than a century ago by Georg Cantor...

Levels: High School (9-12), College
Languages: English
Resource Types: Games, Articles
Math Topics: Infinity, Number Theory

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