Date: Mar 24, 2013 3:39 PM
Subject: Re: Matheology � 224
WM <email@example.com> wrote:
> On 23 Mrz., 18:48, David R Tribble <da...@tribble.com> wrote:
> > WM wrote:
> > >>... consider the list of finite initial segments of natural numbers
> > > 1
> > > 1, 2
> > > 1, 2, 3
> > > ...
> > > According to set theory it contains all aleph_0 natural numbers in its
> > > lines. But is does not contain a line containing all natural numbers.
> > > Therefore it must be claimed that more than one line is required to
> > > contain all natural numbers. This means at least two line are
> > > necessary.
> > That is correct. In fact, all Aleph_0 lines are required
> > (necessary sufficient) to contain all of the naturals.
> That claim is easily disproved.
> For all n in N: The first n lines are neither necessary nor sufficient
> to contain all of the naturals.
> Regards, WM
A red letter day, WM is finally RIGHT about something!
But if David had left out the world "all", and said merely
"In fact, Aleph_0 lines are required
(necessary sufficient) to contain all of the naturals."
then David would have been correct, since EVERY set of aleph_0 lines is
sufficient but no set of less than aleph_0 lines is sufficient.