Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 4, 2013 5:39 PM
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In article
<784a5a95-e5b7-45da-9571-ce0c3245e1a2@5g2000yqz.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Feb., 10:19, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 4, 5:29 am, fom <fomJ...@nyms.net> wrote:
> >
> > > On 2/3/2013 9:20 PM, Virgil wrote:
> > > >> There is no sensible way of saying that 0.111... is more than every
> > > >> FIS.
> >
> > > > How about "For all f, (f is a FIS) -> (length(0.111...) > length(f))" .
> >
> > > In view of WM's positions, length(0.111...) would have
> > > to be the value given to a non-existent.
> >
> > Nope. According to WM the 0.111... is the potentially
> > infinite sequence {.1, .11, .111, ...}
> > It certainly exists
>
> We must be careful. There is no equivalence. 1/9 and 0.111... are both
> finite expressions, finite formulas. Using one of these formulas we
> can calculate every FIS of 0.111..., namely 0.1, 0.11, and so on. But
> from none of the FIS we can obtain 1/9 or 0.111. And the complete set
> of FISs does not exist as the complete string consisting of infinitely
> many 1's (and not only of the formula to calculate each one) does not
> exist.
>
> This nonexistence is so obvious that noone cares. Why else has nobody
> ever used the complete string?
For the same reason that no one writes out the complete string for
10^(100^(1000^(10000^100000))).
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