The better numbering system is Surreal numbers discovered by Conway based on game theory. See http://en.wikipedia.org/wiki/Surreal_number
They are better in this way. Instead of building up the number system from natural, to integer, to rational, to real, etc. we get all of it in one fell swoop by a very simple rule based on arrows pointing up or down depending what branch you take in the progressive bisection of the game moves.
The problem with Surreal numbers is that they have holes in them, but you can do math with the holes, you just cannot integrate. The holes in the Surreal numbers is an example of emptiness, while the origin with no arrows is the Void or the primordial zero.
Surreal numbers are the meta-system to the system of the ordinary numbers built up from various kinds of number that culminates in he real numbers. A meta-system is the inverse dual of the System. Another good thing about them is you get infintesimals and infinities for free. Using Batallie’s terminology from the Accursed Share surreal numbers are a general economy while normal numbers are a restricted economy in which you have to keep adding parts to get it to work.