scholarly journals Surreal numbers, derivations and transseries

2018 ◽  
Vol 20 (2) ◽  
pp. 339-390 ◽  
Author(s):  
Alessandro Berarducci ◽  
Vincenzo Mantova
Keyword(s):  
Surreal Numbers

scholarly journals Recursive surreal numbers.

1990 ◽  
Vol 31 (3) ◽  
pp. 337-345 ◽  
Author(s):  
Leon Harkleroad
Keyword(s):  
Surreal Numbers

Conway's Field of Surreal Numbers

1985 ◽  
Vol 287 (1) ◽  
pp. 365
Author(s):  
Norman L. Alling
Keyword(s):  
Surreal Numbers

Contemporary Infinitesimalist Theories of Continua and Their Late Nineteenth- and Early Twentieth-Century Forerunners

2020 ◽  
pp. 502-570
Author(s):  
Philip Ehrlich
Keyword(s):  
Differential Geometry ◽  
Twentieth Century ◽  
Nonstandard Analysis ◽  
Historical Overview ◽  
Early Twentieth Century ◽  
Late Nineteenth ◽  
Surreal Numbers

The purpose of this chapter is to provide a historical overview of some of the contemporary infinitesimalist alternatives to the Cantor-Dedekind theory of continua. Among the theories we will consider are those that emerge from nonstandard analysis, nilpotent infinitesimalist approaches to portions of differential geometry and the theory of surreal numbers. Since these theories have roots in the algebraic, geometric and analytic infinitesimalist theories of the late nineteenth and early twentieth centuries, we will also provide overviews of the latter theories and some of their relations to the contemporary ones. We will find that the contemporary theories, while offering novel and possible alternative visions of continua, need not be (and in many cases are not) regarded as replacements for the Cantor-Dedekind theory and its corresponding theories of analysis and differential geometry.

Introduction to surreal numbers

1987 ◽  
Vol 28 (1-2) ◽  
pp. 233
Author(s):  
M.D. Kruskal
Keyword(s):  
Surreal Numbers
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