```Date: Feb 19, 2013 10:42 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 19, 4:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> 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, WMLet z be a potentially infinite sequence such thatfor some natural number m, the mth FIS ofz contains a zero.Are z and x coFIS?
```