Date: Feb 4, 2013 5:04 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203
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