An introduction to the theory of surreal numbers / Harry Gonshor.

Format:

Book

Author/Creator:

Gonshor, Harry, author.

Series:

London Mathematical Society lecture note series ; 110.

London Mathematical Society lecture note series ; 110

Language:

English

Subjects (All):

Surreal numbers.

Number theory.

Physical Description:

1 online resource (192 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1986.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; Contents; Preface; Acknowledgements; Chapter 1 Introduction; Chapter 2 Definition and Fundamental Existence Theorem; A. Definition; B. Fundamental Existence Theorem; C. Order Properties; Chapter 3 The Basic Operations; A. Addition; B. Multiplication; C. Division; D. Square Root; Chapter 4 Real Numbers and Ordinals; A. Integers; B. Dyadic Fractions; C. Real Numbers; D. Ordinals; Chapter 5 Normal Form; A. Combinatorial Lemma on Semigroups; B. The ω Map; C. Normal Form; D. Application to Real Closure; E. Sign Sequence; Chapter 6 Lengths and Subsystems which are Sets

Chapter 7 Sums as Subshuffles, Unsolved ProblemsChapter 8 Number Theory; A. Basic Results; B. Partial Results and Unsolved Problems; Chapter 9 Generalized Epsilon Numbers; A. Epsilon Numbers with Arbitrary Index; B. Higher Order Fixed Points; C. Sign Sequences for Fixed Points; D. Quasi e type Numbers; E. Sign Sequences in Quasi Case; Chapter 10 Exponentiation; A. General Theory; B. Specialization to Purely Infinite Numbers; C. Reduction to the Function g; D. Properties of g and Explicit Results; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Bibliography: p. 191.

ISBN:

1-139-88170-1

1-107-36617-8

1-107-37090-6

1-107-36126-5

1-107-36980-0

1-299-40397-2

1-107-36371-3

0-511-89220-9

0-511-62914-1