Virgil
Posts:
4,482
Registered:
1/6/11
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Re: WMatheology � 191
Posted:
Jan 15, 2013 4:12 PM
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In article
<3e51ac5e-0aa6-4c17-8353-d6db63f3a805@ho8g2000vbb.googlegroups.com>,
WM <mueckenh@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.
>
> > 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.
But then I am not constrained by WMytheology
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