Re: abundance of irrationals!)

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.

> This makes absolutely no sense.

Does to me. That you canot think your way out of a wet paper sack, does
not impose any constraints on others.
.

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