Date: Feb 5, 2013 5:37 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<3c52bc20-0b3f-4074-8307-387942aef034@z9g2000vbx.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 5 Feb., 12:17, William Hughes <wpihug...@gmail.com> wrote:

> > On Feb 5, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> > <snip>

> >

> > > So "there is no list of X" is

> > > true for every potentially infinite set.

> >

> > And so it goes. Now there is no list

> > of |N.

>

> Now? Why should there ever have been a complete list, that means a

> complete sequence, that means all terms with all their indices which

> are all natural numbers which do not exist?

If not all natural numbers exist then some of them must not exist.

WHich ones?

> >

> > So ends this round. It has

> > taken 100 posts to get WM to

> > admit that different potentially

> > infinite sets have different

> > listability.

>

> Where had I conceded the complete existence of a list?

Unless every set is listable, there must be sets which are not listable,

so which is it in WMytheology? Is every set listable or are some sets

not listable?

>

> > It would take another

> > 100 posts to get him to admit

> > that he admitted it.

> >

> > We now know

> > that the potentially infinite

> > series 0.111...

> >

> > is not a single line of the list

> >

> > 0.1000...

> > 0.11000...

> > 0.111000...

> > ...

>

> And we know

When WM says "we know" something, it does not mean that anyone other

than WM "knows" it.

> >

> > More importantly, we have learned that

> > we can use induction to show "every"

> > and that "every n -> P(n)" is equivalent

> > to "there is no m such that ~P(m)"

> > So we do not need to resort to "all"

> > to show something does not exist.

>

> Of course, that is true. For instance we can show that no list exists,

> that contains, as indices, all natural numbers.

Then let u see you try to show it without appealing to any of those

"axioms" that only hold in WMytheology and not elsewhere.

And if your believe you have a better set theory than, say, ZF, produce

an axiom system for it of equal clarity to the one for ZF.

Note that, in ZF, if A is a set then the union of {A} with A is also a

set, but apparently this rule does not hold in any set theory in

WMytheology.

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