Date: Apr 5, 2013 1:56 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

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?

Regards, WM