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Topic: Matheology § 191
Replies: 3   Last Post: Jan 12, 2013 6:15 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 191
Posted: Jan 12, 2013 6:15 PM

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

> On 12 Jan., 20:34, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 12 Jan., 16:24, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> > >> WM <mueck...@rz.fh-augsburg.de> writes:
> > >> > Matheology § 191
> >
> > >> > The complete infinite Binary Tree can be constructed by first
> > >> > constructing all aleph_0 finite paths and then appending to each path
> > >> > all aleph_0 finiteley definable tails from 000... to 111...

> >
> > >> >         0
> > >> >       1, 2
> > >> >   3, 4, 5, 6
> > >> > 7, ...

> >
> > >> > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.
> >
> > >> No, it contains aleph_0 * whatever the cardinality of the set of tails
> > >> is.  Talk about begging the question!

> >
> > > A tail can be defined by a finite word *only*. Nobody can quote an
> > > infinite string digit by digit - although most mathematicians believe
> > > that instinctively when pondering about set theory (but never when
> > > doing analysis).

> >
> > That's the part that was missing.  Without it you were begging the
> > question because the set of paths and the set of tails are equinumerous.
> > With it, the argument about tails and finite paths is pointless -- it's
> > just padding around the same tired old claim.

>
> It's only in order to easen the problem for you and others, who are
> comprehending very slowly.

The "problem" is easy enough already, and is only obfuscated by WM's
"easenings".
>
> Paths are solely defined by nodes, according to set theory. (Otherwise
> you could never gather uncountably many.)

They are equally well defined by direction of branchings, as a sequence
of left branching versus right branching.

> Now try to find a path that is missing in the Binary Tree constructed
> by countably many paths.

Until you provide an way of determining whether a path is included in
your set, for example by providing a list of those which you have, we
have no way of determining whether one of ours is also one of your or
not.

Since we have reason not to trust you if we were to present a path to
you, you must provide an independent way for us to test without
accepting you mere word for it

> You fail.

We have not failed until you have provided u with a list of all your
paths or some other way to determines whether you have them all other
than having to take your word for it.

But you cannot so that, so you can never establish your claim.

> But you insist in believing that old nonsense because it is so
> familiar.

We do not believe your nonsense, however familiar it may become, because
it is never supported by valid arguments and often only supported by
trivail ly flawed arguments.

> So you ask for further paths by means of finite definitions like 1/3.
> Therefore I have appended all possible tails to all finite paths
> (which would be sufficient to cover the tree but not sufficient to

Your set of "all possible tails" is itself a provably uncountable
(unlistable) set, as it obviously bijects with the set of all possible
binary sequences.
--

Date Subject Author
1/12/13 Ben Bacarisse
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Virgil