Re: abundance of irrationals!)

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?
>
> > This makes absolutely no sense.
I reiterate.
>
> Does to me. That you canot think your way out of a wet paper sack, does
> not impose any constraints on others.
>
Talking to the mirror again?
--
Smiles,

Tony
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... One of the very root ... >> have in induction, we have an implication that always implies another ... >> the infinite linear set, generally considered the naturals. ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... One of the very root ... > have in induction, we have an implication that always implies another ... > the infinite linear set, generally considered the naturals. ...
    (sci.math)
  • Re: use of real numbers in mathematics and physics
    ... That is not infinite information. ... The pure states then become singular distributions ... > The root of the problem is then addressed by noting that the p's ... > a way framework which will allow for the Bekenstein bound or something ...
    (sci.physics.research)
  • Re: abundance of irrationals!)
    ... >>> For the infinite strings needed to represent paths, ... with the direction being away from the root node. ... A maximal path is one which starts at the root ... > In an infinite binary tree every maximal ...
    (sci.math)
  • Re: Cantor Confusion
    ... far away from the root. ... infinite tree, because that contains edges that are *not* finitely far ... difference between the union of all finite trees and the infinite tree. ... The situation with the rationals is quite different, ...
    (sci.math)