Date: Apr 5, 2013 4:52 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 5 Apr., 22:06, fom <fomJ...@nyms.net> wrote:
> On 4/5/2013 11:22 AM, WM wrote:
>

> > On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote:
>
> >> More precisely.  There is an infinite set of lines D
> >> such that any finite subset of D can be removed.

>
> > How do you call a subset of D that has no fixed last element?
>
> In set theory it is neither a set or a subset


In set theory a set can either be bijected with a FISON or not.

> because the question does not make sense.
>


A subset of D that can be removed without changing the union of the
remaining elements of D can be defined and makes sense.
Examples are the list D
1
1,2
1,2,3
...
and the subset of the first n lines for every n in |N.

So the question makes sense.

> One might compare the remark to a generic set
> of forcing conditions described by the
> information content of their initial sequences.


No claptrap, please. The definition is clear: We consider any subset
of D that can be removed without changing the union of the remaining
elements of D. Does the remaining set of lines have a first line-
number?
Do you reject the theorem that every non-empty set of natural numbers
has a first element? Do you reject proofs by infinite descente? Do you
reject mathematics in favour of matheology?

Regards, WM