Re: Cantor and the binary tree

In article <MPG.1cffdbfb5b61809f989d4b@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1cff9fda6b659940989d2e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > > 1) Each number of (0,1) is given by an UNENDING path stretching over
> > > > infinitely many nodes (bits).
> > > And yet you claim that no node is infinitely far from the root? Wrong.
> >
> > When you can produce a mathematically valid proof that adding 1 to a
> > finite number will produce an infinite number, you may claim that there
> > are nodes infinitely far from the root node, but until then, it is you
> > who are worng
> >
> How do you define the distance from a node to the root, if not by the number
> or
> branches and nodes between them? If this IS how you measure it, then how is
> infinite distance different from "an UNENDING path stretching over infinitely
> many nodes (bits)"? This is what I don't understand. Please elucidate.

There is no node on an infinite path that is infinitely far from the
root, because that are always nodes even farther from the root.
That is what unbounded means, there is no last node!

Think of the real line with root node at zero, add one to get to a
child node from any parent node, with the values in between being the
branches. Voila, an unending path.
.

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