In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 19 Nov., 23:08, Vurgil <Vur...@arg.erg> wrote: > > > > That is my impression of your reaction. But in oder to test it, here > > > is the complete representation of the continued fraction C: > > > > > C = (((...((((((10^0)/10)+10^1)/10)+10^2)/10)+... )+10^n)/10)+... > > > > > Now take the reciproce and find 1/C = 0 or 1/C > 1? Which one is the > > > correct value? > > > > Then C is NOT in the form of a continued fraction at all, at least not > > of any standard type. > > That is of no importance. C is a never ending, i.e. continued > fraction.
"Never ending fraction" and "Continued fraction" are quote different in standard terminology. Of one thing continued fractions can, and often do, end. it is only when they are for irrational numbers that they do not end.
> > > > And WM has provided no reason to suspect that the process has any limit > > at all- > > 1/C is a real number. The question remain: Which one is it? 0, > according to mathematics, or >1 , according to set theory.
Every unending continued fraction, at least in the usual sense of continued fractions, may "converge" to a real number, but that does not apply to the expression you presented, at least until you can show that it matches the usual definition of a continued fraction, which it does not appear to do. So that your claim that it must somehow "converge" to some real number requires a proof that you have clearly not provided. --