Date: Jan 15, 2013 5:12 PM
Subject: Re: WMatheology � 191
WM <firstname.lastname@example.org> wrote:
> 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.
Yes by nodes of digits. Having a node or digit at a particular position
differs from not having one. and that also counts, at least outside
> The infinite sequence is the first that contains all finite n. What
> finite n is missing within the finite terms?
The issue is whether the the finite sequence and the infinite sequence
have the same values at EVERY position, and since the infinite one has
positions the finite one doe not, the two of them can never be the same.
> > > 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.
But 10^-oo is specifically excluded by you, and everything else is NOT
beyond al finite numbers.
> So the limit 1/9 is beyond all finite
But still represented by the totality of terms.
Is 9 - (10^-1 + 10^-2 + 10^-3 + ...) strictly positive?
If so then find a value between it and 0.
> > 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.
I know of many others. 1/2^1 + 1/2^2 + 1/2^3 + ... for example.
Why is yours the first?.
> What finite n is missing within the finite terms?
None of them