Date: Mar 16, 2013 2:38 PM
Subject: Re: Matheology § 224
On 16 Mrz., 19:26, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 16, 7:10 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 16 Mrz., 18:10, William Hughes <wpihug...@gmail.com> wrote:
> > > > Ok, I understand. Anyhow, if the number of lines is not empty, then
> > > > there must remain at least one line as a necessary line.
> > > Not a particular line. This is similar to
> > > the case where any set of lines with an unfindable
> > > last line has at least one "necessary" findable line.
> > > This line has a line number in the original
> > > list but we can choose the "necessary"
> > > findable line to have any line number we want.
> > No, it is always the last line. We call it unfindable or unfixable
> > because as soon as we have found it, it is no longer the last line.
> Note, that I am not talking about the unfindable line,
> but the "necessary" findable line. We can choose this
> line to have any line number we want
In potential infinity there is no necessary line except the last one.
We know that with certainty from induction. Every found and fixed line
n cannot be necessary, because the next line contains it.
Everything that is in the list
1, 2, 3
1, 2, 3, ..., n
is in the last line. Alas as soon as you try to fix it, it is no
longer the last line.
Think of the time. What is "now"? As soon as you try to fix it, it is
past. In time you can predict the development of clocks. In lists
there is no such smooth, predictable evolution. Will the next line
added to above list be n+1, or n^2 or n^n^n^n (all those of course
also including n+1 and its followers? There are no limits. But as soon
as we look onto the last line, we get the idea of another one and that
will add one or many lines to the list.