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Topic: Matheology � 233
Replies: 36   Last Post: Apr 2, 2013 5:56 PM

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Virgil

Posts: 7,025
Registered: 1/6/11
Re: Matheology � 233
Posted: Apr 2, 2013 5:56 PM
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In article
<7ab07dbc-c9b1-48af-8e59-d91cf271b228@c15g2000vbl.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 2 Apr., 02:01, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <1dd2037c-407c-49f6-afc6-e00c1d853...@w21g2000vbp.googlegroups.com>,
> >
> >
> >
> >
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 1 Apr., 22:44, Virgil <vir...@ligriv.com> wrote:
> >
> > > > > You do not believe that a sequence or list of all rational numbers can
> > > > > be constructed?

> >
> > > > One can "enumerate" the set of all rationals by formula, as has been
> > > > quite often done, but not by physically listing all of them.

> >
> > > A formula giving every entry is enough.
> >
> > > > Note that one cannot ennumerate by listing even sufficiently large
> > > > finite sets, so being listable other than by formula is not a relevant
> > > > criterion.

> >
> > > Constructing a list by a formula is enough to prove what I said.
> >
> > And enough to disprove what WM has said as well.

>
> Then try it.
> What did I say?


Among other things, WM has said that in a COMPLETE INFINITE BINARY TREE
there are paths of finite length, but as paths are, by definition, only
MAXIMAL sequences of parent-child linked nodes and EVERY node has child
nodes, there cannot be any such sequence of parent-child linked nodes
which is both finite and maximal.

What WM miscalls paths are merely FISONs (finite initial sequences of
nodes), no one of which fails to be a PROPER subset of some other FISON,
and thus cannot be maximal and thus cannot be a path.
--





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