As many who are into recreational mathematics may have heard about, there is a certain class of numbers which defies all intuition even among those who have worked with the likes of the infinitesimals found in calculus or the transfinite ordinals and cardinals contained within set-theory. These numbers are truly so out of this world they have been called surreals for a reason.
When researching surreal numbers however, a friend wished to know how they are related to games of Hackenbush. Frankly I've always more interested in trying to understand the technical definition of surreals than with some stick-figure game, but putting all hesitancy to the wayside, I will explain how both work to form the marvelous class of numbers John Horton Conway made.
This post will be written as I compile information from various sources about the surreal numbers, eventually culminating in an easy-to-understand guide to surreals that hopefully covers every conceivable question regarding their nature and formation.