Date: Mar 20, 2013 11:24 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 20 Mrz., 14:00, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 20, 1:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> <snip>
>

> > > So your proof that any two lines can be replaced
> > > by one line without changing the contents is irrelevant.

>
> > Since contents can only exist in lines, and since every line is
> > superset to all its predecessors, the proof is correct.

>
> The proof is irrelevant (it is, however, correct)


Nice to hear. Not that I had any doubt, but it is nice to hear that
you have no doubt too.

> since showing that lines are not needed for their
> contents does not show that the lines are not needed.


The lines were invented by myself solely for this purpose.

The first question is:
Is the first line necessary to have the number 1 in the list.

Formulated somewhat more "mathematically":
Is the union of all lines different from the union of all lines except
the first one.

Then go to the second question.

> To show that actual infinity is unreasonable you
> have to show the lines are not needed.


I show that every line, that is not the last line, is not needed.
Since there is not a last line in actual infinity, this shows that all
lines are not needed.

The unreasonable argument is this: "There are all lines, but there is
no last line." It has been pasted together from: Every natural number
can be regonized as such. For every natural number there is a next
one.

Regards, WM