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. Alberto Monteiro
