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


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