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Re: Matheology § 203
Posted:
Feb 4, 2013 5:04 AM
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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?
Regards, WM
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