Date: Apr 5, 2013 2:24 AM
Author: fom
Subject: Re: Matheology § 224

On 4/5/2013 12:56 AM, WM wrote:
> On 4 Apr., 23:08, William Hughes <> wrote:
>> On Apr 4, 10:45 pm, WM <> wrote:

>>> On 4 Apr., 20:57, William Hughes <> 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.