Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 190
Replies: 15   Last Post: Jan 14, 2013 3:35 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 190
Posted: Jan 12, 2013 6:26 PM

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

> On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > Matheology 190
> >
> > > The Binary Tree can be constructed by aleph_0 finite paths.
> >
> > >         0
> > >       1, 2
> > >   3, 4, 5, 6
> > > 7, ...

> >
> > Finite trees can be built having finitely many finite paths.
> > A Complete Infinite Binary Tree cannot be built with only finite paths,
> > as none of its paths can be finite.
> >

> Then the complete infinite set |N cannot be built with only finite
> initial segments {1, 2, 3, ..., n} and not with ony finite numbers 1,
> 2, 3, ...? Like Zuhair you are claiming infinite naturals!

A finite initial segment of |N is not a path in the unary tree |N.

And neither |N as a unary tree nor any Complete Infinite Binary Tree
has any finite paths.

"A Complete Infinite Binary Tree cannot be built with only
finite paths, as none of its paths can be finite."

Means the same as

"A Complete Infinite Binary Tree cannot be built HAVING only
finite paths, as none of its paths can be finite."

WM has this CRAZY notion that a path in a COMPLETE INFINITE BINARY TREE
can refer to certain finite sets of nodes.

And no one is claiming any infinite naturals, only infinitely many
finite naturals.
--