Date: Feb 5, 2013 6:17 AM
Author: William Hughes
Subject: Re: Matheology § 203
On Feb 5, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> So "there is no list of X" is
> true for every potentially infinite set.
And so it goes. Now there is no list
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
is not a single line of 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.