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.
