Introduction to Non-Wimpy Number Systems

A non-credit IAP mini-course consisting of three lectures. January 7-9.

Course description: Finite numbers are wimpy. Learn how to construct and play with two extensions of the real number system that contain infinite and infinitesimal numbers.

Wednesday January 7. The Hyperreal Numbers. Introduces Abraham Robinson's Hyperreals and illustrates their use in a formulation of probability theory that allows for events with infinitesimal probability. Lecturer: Adam Elga.

Thursday January 8. Arithmetic of Combinatorial Games. Provides a background for the study of the Surreal numbers by examining the ordering and arithmetic of combinatorial games. We will then illustrate with a more in-depth study of the special class of impartial games. Lecturer: Jacob Lurie.

Friday January 9. The Surreal Numbers. We will construct the surreal numbers from the sign sequence point of view, then describe the relationship between this and their game-theoretic origins. We will discuss the algebraic structure on the surreals with emphasis on the case of addition. Lecturer: Jacob Lurie.

All lectures begin at 2pm at room 37-212.
Instructors: Adam Elga, Jacob Lurie

Last revised: October 4, 1997
Adam Elga | adam@mit.edu | MIT