Date: Mar 24, 2013 4:29 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<729f073f-8948-4eb9-991a-2bd249ac5d95@c6g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Mrz., 16:19, William Hughes <wpihug...@gmail.com> wrote:
> > On Mar 24, 4:09 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >

> > > On 24 Mrz., 14:42, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Mar 24, 12:13 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 24 Mrz., 11:02, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > On Mar 24, 10:23 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > > > On 23 Mrz., 23:58, William Hughes <wpihug...@gmail.com> wrote:
> > > > > > > > WH: this does not mean that one can do something
> > > > > > > > WH: that does not leave any of the lines of K
> > > > > > > > WH: and does not change the union of all lines.

> >
> > > > > > > This does not mean that one can really do so
> >
> > > > > > It does, however, mean that you have not shown
> > > > > > that one can or cannot.

> >
> > > > Have you shown that "one can or cannot".
> >
> > > > Yes or no please.
> >
> > Please answer the question.

>
> I did so. Given ZFC: one can - but in fact: one cannot.


But since everyone has been given both ZF and ZFC, if they wish it,
everyone can.
>
> Please answer this question (the best way for our readers to
> understand the difference between pot. and act. infinity):
> What is the difference between the Binary Tree that constains only all
> finite paths and the Binary Tree that contains in addition all
> actually infinite paths?


A binary tree that contains only "all finite paths" cannot exist, at
least not outside Wolkenmuekenheim.

A binary tree that contains one path of each positive natural number
length will necessarily also contain exactly one path of infinite length.

A complete finite binary tree must contain 2^n paths each of length n
(having n + 1 nodes) for some natural n.

A complete infinite binary tree must contain 2^aleph_0 paths each of
length aleph_0 and having aleph_0 nodes.
(having n_1 nodes) for some natural n.

No other sorts of complete binary trees are possible.
>
> Regards, WM

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