Date: Feb 19, 2013 10:15 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 19 Feb., 14:10, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 19, 12:41 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 18 Feb., 23:08, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Feb 18, 10:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 18 Feb., 19:19, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > Is there a potentially infinite sequence,
> > > > > > > x, such that the nth FIS of x consists of
> > > > > > > n 1's

>
> > > > 1
> > > > 11
> > > > 111
> > > > ...

>
> > > > > > Yes, of course
>
> > > > > Let y be a potentially infinite sequence
> > > > > where the nth FIS of y consists of a 1 followed
> > > > > by n-1 0's

>
> > > > 1
> > > > 10
> > > > 100
> > > > 1000
> > > > ...

>
> > > > > Are x and y coFIS?
>
> > > > No.
>
> > > Is y the first line of the potentially
> > > infinite list of potentially infinite
> > > sequences

>
> > > L=
>
> > > 1000...
> > > 11000...
> > > 111000...
> > > ...

>
> > > ?-
>
> > The n-th term of y and of the first line of L are coFIS up to every n.
>
> If two potentially infinite sequences have the same FIS's
> up to every n then they are coFIS.
>
> The concept "coFIS up to n" has not been and need not be defined.


It is self-evident that "for every natural number" is identical with
"up to every natural number". More than "up to number n" with n a
natural number not fixed though is not a meaningful expression in this
connection.

>
> Are y and the first line of L coFIS?-


Yes, obviously.

Regards, WM