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 | | MIT