Table of Contents - 15.1. Sign sequence representation and Alling's axioms
The surreal numbers can be represented in several equivalent ways. In
[Alling], Norman Alling made this notion explicit by giving a set of axioms
that all representations admit, then proving that there is an order and
birthday preserving bijection between any systems that satisfy these axioms.
In this section, we start with the definition of surreal numbers given in
[Gonshor] and derive Alling's axioms. After deriving them we no longer refer
to the explicit definition of surreals. In particular, we never take
advantage of the fact that the empty set is a surreal number under our
definition.