Date: Apr 5, 2013 4:40 AM
Author: Virgil
Subject: Re: Matheology � 224

In article <EbednT0U7oa488PMnZ2dnUVZ_rKdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 4/5/2013 12:56 AM, WM wrote:
> > On 4 Apr., 23:08, William Hughes <wpihug...@gmail.com> wrote:
> >> On Apr 4, 10:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >>

> >>> On 4 Apr., 20:57, William Hughes <wpihug...@gmail.com> wrote:
> >>
> >> <snip>
> >>

> >>>> A collection need not share a property
> >>>> that every one of its elements has. In this case
> >>>> every one of the elements of the collection has the property
> >>>> that it can be removed without changing the union.
> >>>> The collection does not have this property.

> >>
> >>> That is impossible if all elements can be removed.
> >>
> >> Nope. Any single element can be removed. This does not
> >> mean the collection of all elements can be removed.

> >
> > Does the axiom of infinity result in an infinite set? Or can only any
> > single element be added by the prescription: If a is in N, then {a} is
> > in N too?

>
> WM is always claiming knowledge of ZFC.
>
> Stupid questions deserve stupid answers.
>
> The word "added" suggests an activity that
> is not described by the formal language used
> to axiomatize ZFC set theory.
>
> There is a reason set theory and other mathematical
> theories were given formal axiomatizations.


Axiom systems eliminate the sort of wiggle room that people like WM
cannot operate without.
--