Date: Feb 15, 2013 5:58 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

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