Date: Mar 24, 2013 7:48 AM
Subject: Re: Matheology § 224
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.