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},

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