Of course you can always use Conway's surreal numbers (http://en.wikipedia.org/wiki/Surreal_number).

I can only recommend reading his book 'On Numbers and Games':

"On Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a preeminent mathematician, and is directed at other mathematicians. The material is, however, developed in a most playful and unpretentious manner and many chapters are accessible to non-mathematicians." (http://en.wikipedia.org/wiki/On_Numbers_and_Games)