Virgil
Posts:
4,491
Registered:
1/6/11
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Re: Mathematics in brief
Posted:
Dec 9, 2012 5:00 PM
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In article
<ea02c482-ead0-48f6-99ce-681ea7b96360@f4g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 9 Dez., 10:41, Zuhair <zaljo...@gmail.com> wrote:
> > On Dec 9, 11:35 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 9 Dez.,
> > 05:55, Zuhair <zaljo...@gmail.com> wrote:
> >
> > > > You need to prove that the set of all paths is countable, and so far
> > > > you didn't present a proof of that.
> >
> > > The set of all finite paths is countable. Therefore it is not possible
> > > to define an infinite path by adding nodes to any finite path. All
> > > nodes to be added are already in finite paths. Therefore, by following
> > > the nodes of a path, you never define an infinite path. It is
> > > interesting that practically everybody not yet brainwashed can
> > > understand that.
> >
> > Every node is reachable by a finite path, that's correct. But that is
> > irrelevant
> > here, we are speaking here about the number of all "path"s in the
> > Binary Tree
> > and not about the number of all nodes. we know that the number of all
> > nodes
> > is countable, the question is: is the number of all paths (finite and
> > infinite)
> > is countable?
>
> So it has become obvious now, that is not possible to define "all
> paths" by nodes. Only the finite paths can be defined by their nodes.
> How can you define all paths if not by nodes?
One defines the set of all paths as the set of all functions from |N to
{m,w}. Then any function from |N to {m,w} is a path.
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