Re: abundance of irrationals!)

Virgil said:
> In article <MPG.1ceedd05baefca52989c51@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1ceea621fe0d3b63989c3a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > 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,
> > >
> > > Yes!
> > >
> > >
> > > > and both closer
> > > > than the branch they define?
> > >
> > > NO, each node (ecexcept the root node) is at the _farther_ end of the
> > > branch which extends to it.
> > So, that branch infinitely far from the root, has a node at the end of it
> > that
> > is closer to the root than it is?
>
> No!
>
> If any node or branch were to be infinitely far from the root, so would
> be all nodes and branches attached to them by any finite chain of nodes
> and branches, so would still be just as far away.
>
And if they were attached by an infinite path, they could be finitely away from
the root. So? What is that supposed to prove?
--
Smiles,

Tony
.

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