Surreal numbers - a new number system for the new millenium

The mathematical world hasn't yet appreciated the advent
of a marvelously enlarged and improved number system, J H Conway's
surreal numbers.  In a compellingly simple and natural way, they
simultaneously encompass the usual real numbers, Cantor's ordinal
numbers, and a slew of engendered numbers of enormously varied sizes.
(For the first time we have genuine full-status infinitesimals - pace
A Robinson ... also Bishop Berkeley).  They may be expected to play a
large and increasing role in analysis and other branches.