On 15 Jan., 22:12, Virgil <vir...@ligriv.com> wrote: > In article > <3e51ac5e-0aa6-4c17-8353-d6db63f3a...@ho8g2000vbb.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 15 Jan., 19:45, Virgil <vir...@ligriv.com> wrote: > > > > > That does not help. It can only differ at finite places. > > > > It takes infinitely many finite "places" to make an infinite sequence. > > > That does not help you. There are infinitely many finite initial > > sequences such that no finite combination of nodes or digits is > > missing. > > But every infinite combination is missing so any infinite combination > differs from every finite combination.
Not by nodes or digits. And that is what counts in mathematics. > > > > > > > > > > And it is quite legitimate to speak of some property as belonging to > > > "ALL" of those "places" outside of WMytheology, even though the set of > > > such "places" must be an infinite set. > > > The the following sequence must have all natural numbers as negative > > exponents: > > > 1) 10^-1 > > 2) 10^-1 + 10^-2 > > 3) 10^-1 + 10^-2 + 10^-3 > > ... > > oo) 10^-1 + 10^-2 + 10^-3 + ... (not containig 10^-oo) > > > And they all must be in one line. But that line does not exist. There > > exists only the limit 1/9. But 1/9 is not a term of this sequence. It > > differs from the sequence by having all natural numbers as negative > > exponents. > > You prove my point that the infinite sequence is different from every > finite sequence. > The infinite sequence is the first that contains all finite n. What finite n is missing within the finite terms? > > > > Alas, how can there be all finite terms of the sequence, enumerated by > > all finite natural numbers, whereas all natural numbers as exponents > > already are beyond the finite terms? > > Which terms in your > "oo) 10^-1 + 10^-2 + 10^-3 + ... (not containig 10^-oo)" > are "beyond all finite terms"?
oo is beyond all finite numbers. So the limit 1/9 is beyond all finite terms. > > I do not find anything in it that is beyond all finite terms.
The infinite sequence of 1/9 is the first that contains all finite n. What finite n is missing within the finite terms?