An Analysis of The Surreal Number System

Authors

Aaron C. Brown, The College of WoosterFollow

Abstract

The surreal numbers are an enormous and extensive class of numbers. The surreals contain familiar numbers such as integers and real numbers, along with less familiar numbers such as ordinals or strictly surreal numbers. Importantly,all surreal numbers can be represented as a specific combinatorial game known as Hackenbush. In this paper, we will explore the relationship between Hackenbush and the surreal number system, which will be useful for constructing the surreal numbers. Additionally, we will explore algebraic properties of the surreal numbers (e.g. transitivity, reflexivity, etc.) and surreal operations such as addition and multiplication.

Advisor

Moynihan, Matthew

Department

Mathematics

Recommended Citation

Brown, Aaron C., "An Analysis of The Surreal Number System" (2017). Senior Independent Study Theses. Paper 7571.
https://openworks.wooster.edu/independentstudy/7571

Disciplines

Analysis

Publication Date

2017

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis