Re: Cantor and the binary tree

Virgil said:
> In article <MPG.1d078685cadd6757989da2@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1d064ba0bef27db0989d7f@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > Virgil said:
> > > > > In article
> > > > > <MPG.1d013364b1ff65ec989d70@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > > > > Except that no such "infinitely far from the root" node can
> > > > > > > exist and still be in any path that starts at the root
> > > > > > > node. It must be in some other tree entirely.
> > > > >
> > > > >
> > > > > > Why? Is there some definition buried in your axioms that says
> > > > > > trees can only be finite?
> > >
> > > What has trees being finite to do with nodes being connected?
>
>
> > You just said, above, that a node infinitely far from the root, which
> > is a requirement of any infinitely long path, couldn't be in the same
> > tree as the root.
>
>
> I did not say that. I have steadfastly denied that there is any node
> infinitely far from the root node in any binary tree, finite or infinite.
You said "it must be in some other tree entirely." You obviously dn't believe
in infinitely loong paths then, or infinite binary trees. You really need to
study some other areas of math and recover whatever sense you may once have
had.
>
> That presumption that unbounded implies infinitely large is a part of
> TO's delusions about infinity, and no part of any valid mathematics.
>
>
> > That seems to imply you can't have infinite trees,
> > since infinite paths are what defines them. What the hell else did
> > you mean? You're not making sense.
>
> I am making perfectly good sense to those not presuming the falsehood
> that unending paths have to contain nodes with infinitely many other
> nodes between them.
How else do you define them as infinite?
> > >
> > > To get from amy point to any other point, one must follow a road of
> > > nodes and branches, and such roads are finite.
>
> > Not in an infinite tree or infinite path, you numbskull.
>
> On every binary tree!
>
> If TO wishes to define other sorts of trees, he is free to do so, but as
> binary trees are presently defined, if yoou can't get from node A to
> node B in a binary tree of any size infinitely many steps you can't get
> there at at all.
> > > > >
> > > > > NO! Only that any connection between 2 nodes must be finite.
> > >
> > > > Says who?
>
> Says everybody with a decent knowledge of trees.\
I have a computer science dagree and a lot of experience working with trees and
lists and various other data structures. In a finite computer, what you say is
true. But if you're talking about an infinite tree, with infinitely long paths,
the definition of that is that the path contains infinitely many nodes and
branches. That's how the length of a path is maeasured: in branches as units.

Maybe your friends get their decent knowledge of trees by climbing them and
scratching their ass on them.
>
> > >
> > > Says everybody who knows anything about it.
> > Name sources or provide some evidence that an inifnitely long path of
> > branches and nodes doesn't contain any pair of nodes with an infinite
> > number of nodes between.
>
> Name sources and provide evidence for your insanity, TO.
So, then, you can't offer any supporting axioms, mathematics, or raw logic to
justify your claim, and you call me crazy, instead of just saying so. Yup.
Typical Virgility.
>
> > You should give this up before you really lose face.
>
> If you think this is a matter of losing face, you are totally off base.
>
> This is a matter of finding what follows from a set of axioms and
> definitions.
You mean like absurd and patently false conclusions? Yes, it's about that.
>
> These axioms and definitions provide for a non-finite set of finite
> natural numbers. They specifically exclude either the necessity or the
> possibility for any non-finite natural numbers.
Then the axioms are flawed, in the ways I have specified.
>
> In the same way one can have an infinite path in which each node is a
> natural and each branch is the successor operation conecting two
> consecutive naturals.
You think like a snail moves.
>
>
> > > I have not denied that there are infinite sets, in fact I have
> > > insisted on them. What I have denied is that there is any way to
> > > add 1 to a finite quantity are get an infinite quantity.
>
> > Dumbass, I never disagreed with that, despite your repeated
> > assertions that that's my position. Stop lying.
> > >
> > > I have offered many valid arguments.
> > >
> > > Only vallid in TO's mind.
>
> > > > > But since all reals (rationals) can be finite, and every
> > > > > natural is also a real(rational), why do any naturals have to
> > > > > be non-finite?
> > >
> > > > Because you have a non-finite set of them, and every one adds 1
> > > > to the range of values in the set.
> > >
> > > Which "add 1" steps beyond the finite?
>
>
> > The infinite sum of them, stupid.
>
> There are no such things as infinite sums of them.
There are no such things as infinite sums? Uh huh. Whatever you say.
>
>
>
>
> > You are so dumb that that's the way you see it. Your ego problems get
> > in the way of your mind. That's probably because of your lack of
> > understanding of your place in the midst of the Infinity around you.
> > Grow up.
>
> When one can no longer attack the logic, one is reduced to attacking the
> man.
Yes, that's why you have been making dishonest insulting remarks about me for
weeks, and changing the subject as often as possible, reponding to questions
with insults, and generally being an ***. Learn to think for a change, and
to play nice in the sandbox.
>
> Sure sign of losing the argument!
Sure sign of being fed up with a little prig.
>

--
Smiles,

Tony
.

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