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Topic: Matheology § 170
Replies: 41   Last Post: Dec 8, 2012 5:35 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 170
Posted: Dec 8, 2012 5:35 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 8 Dez., 09:41, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  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.
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