bases can be in any form you want, you can have negative bases, rational bases, irrational bases, imaginary bases, it doesn't matter.
Yes base pi is a real number system, where the value of pi is one, and there are nontrivial cases where it would be useful to operate in a base pi system.
It should be noted that in non-integral bases, there tend to be numbers with multiple significantly different expansions. I don't know an example for base Pi off the top of my head, but for base sqrt(2), twelve would be 1010000 or 10000000.0100...(goes on in an irregular fashion).
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Anonymous2006-10-23 6:37
>>48 I don't know an example for base Pi off the top of my head
uh, how about 1 (aka 0.3011...)?
So what's the point of using 'base pi' instead of just writing eg 1 = 3/pi+1/pi^3+1/pi^4...