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