In article <email@example.com>, WM <firstname.lastname@example.org> 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. > > > 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. > > 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"?
I do not find anything in it that is beyond all finite terms.