Re: abundance of irrationals!)

Virgil said:
> In article <MPG.1ced4405db67c460989c30@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
>
> > > > Perhaps you mean a string of such
> > > > connections, in which case that is also specified by the string of digits
> > > > denoting each number, 0 for left branch and 1 for right.
> > >
> > > That would be a path. A maximal path is one which starts at the root
> > > node and either ends at a terminal node from which no further branches
> > > extend, or does not stop at all.
> > >
> > > In an infinite binary tree (with no finite maximal paths) every maximal
> > > path contains an infinite sequence of branches.
> > >
> > > Each node corresponds to the finite path starting at the root node and
> > > ending at the given node, so there are only countably many nodes
> > > coreesponding to those countably many finite paths.
> > >
> > > But there are uncountably many maximal ( and therefore inifinte) paths
> > > in an infinite binary tree as defined above.
> > >
> > Holy cow!! Do you ever listen to yourself, or critically examine what you are
> > told?
>
> Much better that TO does.
> >
> > You have infinite maximal paths, with branches infinitely far from the root
> > node, but the nodes they connect are a finite distance from the root?
>
> In an infinite path, each branch and each node is only finitely far from
> the root node, just as in the naturals, each n in N is finite.
You mean in the sense that those two statements are equally illogical? Sure.
What exactly do you mean by "an infinite path", if not a path with an infinite
number of nodes and branches? Please define.
>
> No two nodes can have infinitely many branches or nodes between them and
> still be connected. Every connection between two nodes anywhere in any
> tree is by a finite sequence of braches and nodes.

Not in an infinite tree or on an infinite path. What IS an infinite path, or
tree, on your planet?

>
> > This is almost enough to make me drink the water, or maybe something
> > stronger.
>
> If such truths are too strong for you, avoid mathematics.
"TRUTHS"!!! LMAO. "too strong"! oy, the smell maybe.
>

--
Smiles,

Tony
.

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