```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 anatural number not fixed though is not a meaningful expression in thisconnection.>> Are y and the first line of L coFIS?-Yes, obviously.Regards, WM
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