Re: measuring systems (was: Selenites)

At 17:54 29/09/98 -0400, you wrote:
>Pablo Flores scripsit:
>
>> (May a number be irrational in one base and rational in
>> another one? Math teachers/students out there?).
>
>No.  Rational/irrational is a property of a number, not of its
>representation.
>
        A rational is a number you can make into a fraction of two integers,
whatever its decimal representation. So 1/10 : 0.1 is rational, and 1/3 :
0.3333333333333333... is also rational. The irrational numbers are the other
ones, like Pi, the square root of 2, etc... So it doesn't depend on the base.

        If you want to make fraction in a base different from decimal, you
have to use only the numbers you can use in this base. So, in binary system,
1/3 would be 1/11 (3 is 11 for a computer). Also, you can make comma numbers
with powers of the base. For instance, in base 2, 0.10101 would be
0*2^0+1*2^-1+0*2^-2+1*2^-3+0*2^-4+1*2^-5=1/2+1/8+1/32=21/32 (I think its
representation in decimal system is infinite). 0.10101 would be in fraction
10101/100000.

        As you can see, you can use fractions or "decimal" numbers in every
base with the same rules you use for the decimal system. We find it
difficult because we use only the decimal system in every day life.



>--
>John Cowan                                      cowan@ccil.org
>                e'osai ko sarji la lojban.
>
>
                                                Christophe Grandsire
                                                |Sela Jemufan Atlinan C.G.

homepage: http://www.bde.espci.fr/homepage/Christophe.Grandsire/index.html