**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 a effort to be agnostic
towards
the exact implementation of surreals. (Contributed by Scott Fenton,
9-Jun-2011.) |