Date: Dec 8, 2012 5:35 PM
Subject: Re: Matheology � 170
WM <firstname.lastname@example.org> wrote:
> On 8 Dez., 09:41, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <087b4922-8254-4cad-9246-70ea50c79...@a2g2000yqh.googlegroups.com>,
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 7 Dez., 22:53, Virgil <vir...@ligriv.com> wrote:
> > > > > Just that can be constructed by one angle and two complete sides.
> > > > I note that WM acknowledges that those sides are required to be
> > > > COMPLETE, But in his example they are not, since they both lack
> > > > endpoints at their other (not in common) ends.
> > > Interesting. But you believe that the natural numbers form a complete
> > > set without an endnumber?
> > The naturals have only one 'end number' that is itself a natural, the
> > first.
> > Every other natural but thate first is between yet other naturals.
> > So the set is complete as a set,
> And it has a cardinal number. So is the set of lines of my
> arithmetical triangle complete and has a cardinal number. But this
> cardinalk number multiplied by the unit length is no longer a number?
The first natural is an end number of the naturals is an end number
because it is a natural which precedes all other naturals in the
standard ordering. There is no equivalent natural that follows all other
naturals is standard ordering. While omega or aleph_0 may be considered
as upper bounds on initial sets of naturals, neither is a member of that
set of naturals, so is not a terminal member, as required.