In article <fc951903-96d1-42bf-a9be-bbeffb9448f5@w7g2000yqo.googlegroups.com>, William Hughes <wpihughes@gmail.com> wrote:
> 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. > > So WMs statements are > > there is a line l such that d and l > are coFIS > > there is no line l such that d and l > are coFIS
Of course, everywhere outside of Wolkenmuekenheim, lines being coFIS would be equal, but Wolkenmuekenheim is such a weird place that only WM, its creator, can speak for what goes on in it. --
