Date: Mar 8, 2013 10:55 AM
Subject: Re: Matheology § 222 Back to the roots
On 8 Mrz., 15:45, William Hughes <wpihug...@gmail.com> wrote:
> WM: There does not exist
> (in the sense of not findable)
> a natural number m such that
> the mth line of L is coFIS with
> So let's talk about d the way you
> talk about d.
That is the origin of many misunderstandings.
d does exist as "the diagonal". Compare: The sequence (1/n) does
exist, namely by the finite definition "The sequence (1/n)" with the
obvious understanding that n assumes every natural number or even all
natural numbers one ofter the other.
In this sense we can talk in analysis and potential infinity about d.
But neither this wording nor any mathematical construction can yield
more than d_1, ..., d_n (for every n).
In this sense (and obviously) every FIS of d is a line. So we have
identity between FIS of d and corresponding lines. It is simply
impossible that d (and that means "any FIS" of d in pot. inf.) is
longer than every line.