```Date: Jan 13, 2013 4:51 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 191

On 13 Jan., 22:45, Virgil <vir...@ligriv.com> wrote:> In article> <bf5b8afa-bd4d-4f8e-9414-ff26ba2b7...@w8g2000yqm.googlegroups.com>,>>  WM <mueck...@rz.fh-augsburg.de> wrote:> > There are not uncountably many finite (initial segments of) paths. And> > also any anti-diagonal can only differ from other paths in its (and> > their) finite initial segments. Unless your silly idea of nodes at> > level aleph_0 was correct (it is not) there is no chance to differ at> > other places than finite (initial segments of) paths. But that is> > impossible if all of them are already there. And the latter is> > possible, because they form a countable set.>> A set which WM cannot count!Even you can count it!    0  1  23 4 5 6...>> The definition of a set being countable is that there is a surjection> from |N to that set.>> Thus in order to PROVE a set is countable one must show a surjection> from |N to that set, which is just a listing, possibly with repetitions,> of that sets members.>> But any listing of the paths of a Complete Infinite Binary Tree (as> infinite binary sequences) proves itself incomplete.>> Thus the set of paths cannot be made to fit the "countable" definition.Above you see the enumeration of the set0.0.00.10.000.010.100.11...Regards, WM
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