Re: abundance of irrationals!)

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.
.

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