surreal numbers
each number is {L|R} where every element of L is less than every element of R
each number is a game, L is the set of moves for the left player and vice-versa. A player who has no move loses.
a number may have many representations
{|} = 0 {0|} = 1 {1|} = 2 …
{|0} = -1 …
{0|1} = 1/2 …
{0,1,2,…|} = w {0|1,1/2,1/4..} = e