Surreal Birthdays and Their Arithmetic

TL;DR

This paper explores how arithmetic operations on surreal numbers relate to their recursive construction, revealing simple rules governing their birthdays during these operations.

Contribution

It demonstrates that birthday arithmetic for surreal numbers adheres to straightforward, predictable rules, enhancing understanding of their recursive structure.

Findings

Birthday arithmetic follows simple, consistent rules.

Arithmetic operations affect birthdays in predictable ways.

Provides insights into the recursive nature of surreal numbers.

Abstract

Surreal numbers are created recursively, with the "birthday" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday arithmetic follows simple rules.