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 § 198
Replies: 40   Last Post: Jan 26, 2013 6:54 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 198
Posted: Jan 25, 2013 3:18 AM

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

> On 25 Jan., 01:27, William Hughes <wpihug...@gmail.com> wrote:
> > On Jan 24, 8:52 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >

> > > The following is copied from Mathematics StackExchange and
> > > MathOverflow. Small wonder that the sources have been deleted already.

> >
> > > How can we distinguish between that infinite Binary Tree that contains
> > > only all finite initial segments of the infinite paths and that
> > > complete infinite Binary Tree that in addition also contains all
> > > infinite paths?

It is easy, the former does can exist at all outside of WMytheology,
while the latter can only fail to exist within WMytheology.
> >
> > > Let k  denote the L_k th level of the Binary Tree.  The set of all
> > > nodes of the Binary Tree defined by the union of all finite initial
> > > segments (L_1, L_2, ..., L_k) of the sequence of levels U{0 ... oo}
> > > (L_1, L_2, ..., L_k) contains (as subsets) all finite initial segments
> > > of all infinite paths. Does it contain (as subsets) the infinite paths
> > > too?

What WM rejects is the binary equivalent of having the union of all
finite initial segments of naturals equal the infinite set of naturals,
|N
> >
> > > How could both Binary Trees be distinguished by levels or by nodes?

> > They can of course be distinguished.
> >
> > In one case you do not include infinite subsets.
> > In the other you do.

>
> My question aimed at the posiibility to distinguish the Binary Trees
> by a mathematical criterion, namely that one that is applied in the
> diagonal argument. Of course you have understood that.

Why would he, or anyone else, "understand" your nonsense?
>
> That does not hinder you to believe in addition in matheological
> concepts that cannot be based on mathematical facts like nodes,
> levels, or digits.

What we find difficult to believe in is a Complete Infinite Binary Tree
which is not in any way infinite, which is the problem with WM's
versions.
--