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