Date: Mar 24, 2013 5:13 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 23 Mrz., 23:36, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 23, 11:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 23 Mrz., 21:26, William hHughes <wpihug...@gmail.com> wrote:
> > You claim that no finite line of the set changes the union.

>
> There is no single finite line such that the removal of this one line
> changes the union.


This holds for every line and all its predecessors, i.e., for the
whole potentially infinite set

1

1
1,2

1
1,2
1,2,3

...


>
> > You claim that when every finite line which does not change the union,
> > is deleted, then the union is changed.

>
> When every finite line with the property that when it alone is
> removed then the union is not changed, is deleted, then the union
> is changed.


That is an unconfirmed statement. And it is wrong, if every well-
defined set of natural numbers has to have a least element. Do you
accept this theorem?
Do you agree that the definition "line of the list that does not
change the union of all lines" is well defined?
>
> This is not equivalent to
>
> There is at least one line l, so that if l is removed the union
> is changed.


See above. Do you reject this order-property of |N? Or do you think it
is necessary to have an excemption for our special case?

Regards, WM