a numbering system devised by John Conway while trying to understand the game of Go.

“The surreal numbers are a class of numbers which includes all of the real numbers, and additional “infinite” numbers which are larger than any real number. They also include “infinitesimal” numbers that are closer to zero than any real number, and each real number is surrounded by surreals that are closer to it than any real number. In this, the surreals are similar to the hyperreal numbers, but their construction is very different and the class of surreals is larger and contains the hyperreals as a subset. Mathematicians have praised the surreal numbers for being simpler, more general, and more cleanly constructed than the more common real number system. ” wikipedia

a basic introduction (basic maths) http://lib.fo.am/pub/Libarynth/SurrealNumbers/surreal_numbers.pdf

explaination by fiction, Donald Knuth → http://www-cs-faculty.stanford.edu/~knuth/sn.html

wikipedia entry http://www.wikipedia.com/wiki/Surreal+numbers

SURREAL NUMBERS and MANY-WORLDS http://www.innerx.net/personal/tsmith/surreal.html