m. m. m.
Posts:
108
Registered:
11/28/11
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Re: The uncountability infinite binary tree.
Posted:
Dec 16, 2012 6:17 PM
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On Dec 16, 3:07 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <d3a3d23d-b0b5-4ffe-bb75-eb6a9a062...@f19g2000vbv.googlegroups.com>,
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> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 16 Dez., 16:54, Rupert <rupertmccal...@yahoo.com> wrote:
> > > On Dec 16, 1:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 16 Dez., 11:54, Rupert <rupertmccal...@yahoo.com> wrote:
>
> > > > > On Dec 16, 11:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > On 16 Dez., 11:02, Rupert <rupertmccal...@yahoo.com> wrote:
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> > > > > > > On Dec 15, 7:07 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > > > On 15 Dez., 16:54, Rupert <rupertmccal...@yahoo.com> wrote:
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> > > > > > > > > On Dec 15, 12:35 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > > > > On 15 Dez., 11:21, Rupert <rupertmccal...@yahoo.com> wrote:
>
> > > > > > > > > > > On Dec 15, 10:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > > > > > > > > > Thus the Infinite binary tree is UNCOUNTABLE.
>
> > > > > > > > > > > > Since it can be proved to be countable, there is a
> > > > > > > > > > > > contradiction.
>
> > > > > > > > > > > How do you prove that it is countable?
>
> > > > > > > > > > First: A Tree that contains all nodes also contains all reals
> > > > > > > > > > of the
> > > > > > > > > > unit interval.
>
> > > > > > > > > > I constrcut the tree, i.e., all nodes, by countably many
> > > > > > > > > > infinite
> > > > > > > > > > paths.
>
> > > > > > > > > Tell us more about this construction.
>
> > > > > > > > I use all finite paths. Every node of the Binary Tree is the end
> > > > > > > > of a
> > > > > > > > path. Then I append these countably many paths by a tail
> > > > > > > > according to
> > > > > > > > my choice. For instance I can use the tail
> > > > > > > > 000...
> > > > > > > > or
> > > > > > > > 010101...
> > > > > > > > or
> > > > > > > > the bit sequence of pi
> > > > > > > > or anything else, for instance a mix of many tails.
>
> > > > > > > > In order to show you that you are dreaming if you think that
> > > > > > > > infinite
> > > > > > > > paths could be identified by their nodes, I don't tell you what
> > > > > > > > tails
> > > > > > > > I have used. If you don't sleep to deep, then you will wake up
> > > > > > > > and
> > > > > > > > recognize that infinite paths are merely defined by finite
> > > > > > > > definitions, and hence belong to a countable set.
>
> > > > > > > > Regards, WM
>
> > > > > > > Okay, so you seem to be saying that you would take all the finite
> > > > > > > paths and append an infinite tail to each one, thereby obtaining a
> > > > > > > countably infinite collection of infinite paths. Is the claim then
> > > > > > > that this would be equal to the collection of all infinite paths?
> > > > > > > Or
> > > > > > > not?-
>
> > > > > > It is equal to the collection of all paths that are defined solely by
> > > > > > their nodes. It is equal to all finite initial strings of digits that
> > > > > > can be applied in a Cantor-list. (Every digit changed there has a
> > > > > > finite index.)
>
> > > > > > Actually infinite paths like that of 0.010101... = 1/3 (in binary)
> > > > > > cannot be defined by nodes. No infinite sequence has ever been
> > > > > > defined
> > > > > > by its terms. Those things have to be defined by finite definitions
> > > > > > like "0.010101..." or "1/3".
>
> > > > > Okay. That all sounds fair enough.
>
> > > > > So, you were going to show us that there are only countably many
> > > > > paths. When are you going to do that?-
>
> > > > First I showed you that there are only countably many paths that are
> > > > defined by nodes. You seemed to agree. Call them the set A.
>
> > > > Well, the other "paths" cannot be defined by nodes. Call them the set
> > > > B. They need definitions by finite words. And there are only countably
> > > > many finite words.
>
> > > > Now consider the union of two countable sets A and B.
>
> > > How do you know that there exists a countable language such that every
> > > path can be defined in this language?
>
> > I do know that in every language (as well as in all languages together
> > since aleph_0 * aleph_0 = aleph_0, and since there are no uncountable
> > languages) only countably many paths can be defined.
>
> But it is quite possible to define a set in which some, even most, of it
> members are so inaccessible that they cannot be individually defined.
>
> E.g., the set of reals.
>
> Thus requiring the members of a set all to be definable before the set
> can be allowed is an invalid objection, at least outside WMytheology.
>
> > What cannot be
> > defined in any language is not a path.
>
> It is if it is a member of a set of paths, regardless of either its
> accessability or definability.
>
> > Therefore I know
>
> False "knowledge" snipped!
> --
I count binary easy because P=NP is easy. No math is hard. P=NP is
easy because P==NP is truth FAST ALGORITHM OR true OUTPUTS "yes" when
the correct answer is "yes" and outputs 'NO' otherwise. I count binary
like so 01=1, 011=2, 0111=3, 01111=4, 011111=5, 0111111=6, 01111111=7,
011111111=8, 0111111111=9, 10=ten or 10 OR 'TEN' or 'yes' otherwise
OUTPUTS "YES" or "yes" AND "no".Musatov->?=Musatov{.}time@ater f n=k
at function=if prelim.pretime-*ater=k-f @if
===MUSATOV.00.--TRUE "KNOWLEDGE" SAVED!> ++musatov
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