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csprof2000
#36
Feb24-09, 09:51 AM
P: 287
"You would use the digits 0 and 1."

Hmmm... alright. Interesting. So you can easily get 0, sqrt(2), 2, 2+sqrt(2), 2sqrt(2), etc.

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.

It seems to be I should be able to divide both sides of the inequality above by 10, leaving
11 > 100, which is oddly enough also true.