Date: Feb 5, 2013 11:08 AM
Author: fom
Subject: Re: Matheology § 203
On 2/5/2013 5:17 AM, William Hughes 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.

>

> So ends this round. It has

> taken 100 posts to get WM to

> admit that different potentially

> infinite sets have different

> listability. 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...

> ...

>

> 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.

>

You are a patient person.