An Introduction to the Theory of Surreal Numbers

These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.

Harry Gonshor (Author)

9780521312059, Cambridge University Press

Paperback, published 18 September 1986

204 pages
22.8 x 15.2 x 1.2 cm, 0.3 kg

The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.

1. Introduction
2. Definition and Fundamental Existence Theorem
3. The Basic Operations
4. Real Numbers and Ordinals
5. Normal Form
6. Lengths and Subsystems which are Sets
7. Sums as Subshuffles, Unsolved Problems
8. Number Theory
9. Generalized Epsilon Numbers
10. Exponentiation
Index.

Subject Areas: Mathematical foundations [PBC]