```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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