Date: Jan 15, 2013 4:29 PM
Subject: Re: WMatheology § 191
On 15 Jan., 22:12, Virgil <vir...@ligriv.com> wrote:
> In article
> 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
> 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?