Quote by csprof2000
Strangely, though, I think that:
110 = 2 + sqrt(2) + 0 ~ 3.4
1000 = 2sqrt(2) + 0 + 0 + 0 ~ 2.8
110 > 1000 in this system.
Is this alright? This seems to go against intuition, but I don't know enough about place value systems to know whether this invalidates it or not. Clearly in any integer base this can never happen... thoughts? Maybe I'm missing something.

This is different from positive integer bases. Also, simplifying the form of a number is different from positive integer bases. (11 + 10 = 21 = 101 in binary, but 11 + 10 = 21 = 1001 in base sqrt(2).) Also Google for "phinary", base phi.