Date: Apr 5, 2013 4:38 AM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<08e5edec-8e86-493a-a0ae-0e74df272234@y12g2000vbh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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?


It merely acknowledges that there are the sets that are the basis of
induction.


> Or can only any
> single element be added by the prescription: If a is in N, then {a} is
> in N too?


Wrong! Again! As usual!

The axiom of infinity says that there is a set containing {} as a member
and such that whenever set a is a member, so is the union of a with {a},
--