 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.
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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.