**Description: **Define the class of
surreal numbers. The surreal numbers are a proper
class of numbers developed by John H. Conway and introduced by Donald
Knuth in 1975. They form a proper class into which all ordered fields
can be embedded. The approach we take to defining them was first
introduced by Hary Goshnor, and is based on the conception of a
"sign
expansion" of a surreal number. We define the surreals as
ordinal-indexed sequences of and , analagous to Goshnor's
and
.
After introducing this definition, we will abstract away from it using
axioms that Norman Alling developed in "Foundations of Analysis
over
Surreal Number Fields." This is done in an effort to be agnostic
towards the exact implementation of surreals. (Contributed by Scott
Fenton, 9-Jun-2011.) |