Surreal Birthdays and Their Arithmetic

Abstract

Summary This paper is about the structure underlying surreal numbers, namely, the birthdays of surreal number forms. The results are intriguing because (i) addition of surreal forms results in simple addition of their birthdays, but (ii) multiplication results in a much more complicated structure of birthdays, given by a kind of two-dimensional Fibonacci sequence. The paper also provides many examples and illustrations designed to help a student become familiar with this interesting set of numbers.