Surreal Numbers

In attempting to evaluate endgames in Go, John H. Conway ran smack into some limitations in game theory. Upon delving into it, it turned out that the problem was the dependence of game theory on real numbers. Conway invented the Surreal Numbers to overcome this roadblock.

In this session, we're going to look at some simple games that Conway, Berlekamp, and Guy use in their book Winning Ways for Your Mathematical Plays to demonstrate valuing games as a sum of their component games. We will talk about how this leads to one formulation of Surreal Numbers. We will look at adding, subtracting, multiplying, and dividing Surreal Numbers. We will also examine some infinitesimal numbers that illustrate why the real numbers are not sufficient for valuing two-player games. We will also look at how the Surreal Numbers handle infinite numbers.