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