On Feb 15, 10:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 15 Feb., 00:44, William Hughes <wpihug...@gmail.com> wrote: > > > > > Two potentially infinite sequences x and y are > > > > equal iff for every natural number n, the > > > > nth FIS of x is equal to the nth FIS of y > > > So we note that it makes perfect sense to ask > > if potentially infinite sequences x and y are equal, > > and to answer that they can be equal if they are actually infinite. > But this answer does not make sense. > You cannot prove equality without having an end, a q.e.d..
A very strange statement. Anyway there is no reason to claim equality. Let us define the term coFIS
Two potentially infinite sequences x and y are said to be coFIS iff for every natural number n, the nth FIS of x is equal to the nth FIS of y.
We note that it makes perfect sense to ask if potentially infinite sequences x and y are coFIS, we have cases where they are not coFIS and cases where they are coFIS.. We also note that no concept of completed is needed, so coFIS can be demonstrated by induction. In particular, you do not need a last element to prove that x and y are coFIS.
