Date: Feb 5, 2013 8:01 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203
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?

>

> 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?

> 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 that there is no line of the list that contains the

potentially infinite sequence of natural numbers or up to which this

is contained in the list.

>

> 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.

Regards, WM