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