> From: Alberto Monteiro <[EMAIL PROTECTED]>
> > The Fool wrote: > > > >> What do you mean by base pi or base e? AFAIK, the definition of > >> base (to represent numbers) means that the base is integer (and >= 2) > > > >What is 3 in base 1? 111 > > > Ah, ok. I forgot about base 1 - maybe because it was the > first base that was used O:-) > > But, pedantically, base 1 can't be defined. We would be forced to write > all numbers as a sum of zero times powers of 1. > > > > >What is 3 in base pi? an irrational number. > > > 3 is still a rational number. I believe you want to say > that 3, if represented as powers of pi - and this can't > be done in a unique way! - would not be a periodic > expression. > > And there's an asymetry here: an irrational but algebraic > number expressed as digits of an integer number is > a non-periodic decimal. An integer number expressed > as digits of an algebraic irrational number is a periodic > decimal. So in converting '3' to base pi what are you solving? An irrational exponent of pi? You can do that but it may not be right. Multiple rational exponents of pi? Multiple irrational exponents of pi?
