In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 3 Mai, 08:47, Zeit Geist <tucsond...@me.com> wrote: > > On Thursday, May 2, 2013 10:47:47 PM UTC-7, WM wrote: > > > > Every finite power of 10 has a reflection at the place n > > > > > = 0: 10^n reflected is 10^-n. This proves that 1/9 has not a decimal > > > > > representation with only finite powers of 10. > > > > It has a representation with only finite powers of 10, > > but it requires an infinite number of these finite powers. > > The number of finite powers does not play a role.
It certainly does. If there were only finitely many finite powers of 10 then 'most' rationals would not have any decimal representations. ] > By the same argument you could require that not all natural numbers > are natural because there are infinitely many of them. Rejected!
That, however, does concede that there are infinitely many of those natural numbers. So WM may be learning something after all! > > > > It is very possible that you are unable to process that > > statement in to something that is possible is a given > > theory. > > In mathematics, this statement is well known.
The actual infiniteness of the set of naturals is certainly well known in mathematics, even though sometimes denied outside mathematics by those entrapped in places like Wolkenmuekenheim. --