Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 198
Posted:
Jan 25, 2013 3:18 AM


In article <ebe4e44929f1456a92c2de2e5c0c842a@k4g2000yqn.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 25 Jan., 01:27, William Hughes <wpihug...@gmail.com> wrote: > > On Jan 24, 8:52 am, WM <mueck...@rz.fhaugsburg.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. 

