Re: abundance of irrationals!)

Virgil said:
> In article <MPG.1ced3bf54b70fa1e989c2c@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > > I didn't disagree that the branches (or paths, as I
> > > called them) are infinitely long. Our disagreement
> > > is this: you think this invalidates my earlier claim
> > > (that each node in the tree is represented by a finite
> > > path) and I do not.
> > if a branch is infinitely long, how long is the string of bits that specifies
> > the node at the end (or finitely close to the end) of that branch? If the
> > node
> > is infinitely far down a branch, it requires infinite bits, one for each
> > fork.
>
> But no nodes are "infinitely far" down a branch. That is the same error
> that TO makes with naturals, assuming that there has to be an infinite
> one. Apparently he does not learn from his mistakes.
>
You said the bracnhes extend infinitely far from the root, but each branch is
bounded by two nodes. Are those nodes, to the near and far side of that
infinitely far away branch, both finitely far from the root, and both closer
than the branch they define? This makes absolutely no sense. I have made no
mistake.

node node ......oo........... branch
^-------------------------------<
--
Smiles,

Tony
.

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