At 02:54 PM 12/14/01, you wrote: >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
But, of course, neither pi nor e is algebraic . . . -- Ronn! :) God bless America, Land that I love! Stand beside her, and guide her Thru the night with a light from above. From the mountains, to the prairies, To the oceans, white with foam� God bless America! My home, sweet home. -- Irving Berlin (1888-1989)
