Re: Cantor and the binary tree

Tony Orlow (aeo6) wrote:
> imaginatorium@xxxxxxxxxxxxx said:
> >
> >
> > Tony Orlow (aeo6) wrote:
> >
> > <snip> ... Here it is again, the standard 'argument':
>
> That was an obnoxious snip. You deliberately snipped the context, where Martin
> said:
>
> > What is it you are smoking? Can I have some? Even in finite binary
> > trees, the number of paths is greater than the number of nodes where
> > branching occurs.
> >
> This is a statement specifically about FINITE binary trees, and it's incorrect.
> Try to be honest from now on, and stop snipping context to make others look
> stupid.

Um, ok, here's the first finite tree I can think of (excuse ASCII-art
problems)

B
| \
| \
X Y

There is one branching node B (bn=1)
There are two paths (B-X, B-y) (p=2)

I believe p > bn. Is this a special case? If you spent less time
spewing out more copies of the same old nonsense, and throwing insults
around you might have time to check some of your statements before you
post them. Or perhaps you just didn't spend the time to read Martin's
statement carefully?


> > > Excuse me Martin, but maybe you should have some of what I am smoking. Every
> > > path ends in a leaf node, which are half the nodes in the tree.
> >
> > An infinite tree means one in which *every* node branches and leads to
> > more paths. However, in a *finite* tree, every path ends in a leaf
> > node. In real mathematics that means that in an infinite tree, every
> > path is unending. But in Orlovian mathematics, any selected statement
> > true of a finite object is also true of an infinite one, and therefore,
> > although the paths never end, they end in leaf nodes.
> Do you see how this statement sounds in the context of what you snipped? Yep,
> pretty dumb.

Which statement? Which part of what I said do you disagree with?

Do you use the term "infinite tree" to mean one in which the paths
never end?

I think you need to give a clear answer to this question, because it is
the root of the problem. Mathematicians use the term "infinite tree",
(or "infinite sequence") to mean something which has no end. If you
believe it "ends at Infinity" then you are talking about something else
(of which you have never given a clear definition, other than some
garbled misuse of what you imagine words like "limit" mean).

You repeatedly advise me to "read up" on infinite series. Since I have
the benefit of a university education in mathematics, which you say you
don't, and since I can see that more or less everything you say is
nonsense, I have to ask where you think I should look for this reading?
Do you have a textbook title and chapter number in mind? You have
several times referred to the Mathworld page on tests for divergence,
though how you think this would help, I don't know.

As for your "three proofs": you repeatedly refer elliptically to
fragments of them. If you are not prepared to select one, then post all
three on a web page somewhere, in what you claim is its finished form.
People will happily point out typos and more serious errors, and you
can repeatedly refine it until you are satisfied it is done (even if
no-one else agrees).

Brian Chandler
http://imaginatorium.org

.

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