Sorry to be opaque but consider this http://www.c3.lanl.gov/mega-math/workbk/map/mpbkgd.html The traditional four color problem but ask the question how many shades of grey are needed to color a map ? Is the answer still four ? If you choose the concept of color with a rational value does the four color problem even make sense ? If you can prove it does how does it relate to the integer problem. This is the problem faced by dark energy/dark matter Are you even asking the right hard questions. Sometimes you have to question the question. Btw it you can answer the above prove its not 42 :) Mike