How to Bake the Real Numbers from Scratch: An Introduction to Surreal Analysis

Based on the work of John H. Conway “On Numbers and Games”. The talk discusses the methods of Dedekind and Khinchin constructing the real numbers. Both assume the existence of some other set (rationals in the case of Dedekind, integers in the case of Khinchin). The elegance of Conway's construction is that the real numbers, and much more, are created with out any assumptions. The "and much more" is the key to winning at checkers and other games.