Re: Cantor and the binary tree



In article <MPG.1cff9fda6b659940989d2e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> > 1) Each number of (0,1) is given by an UNENDING path stretching over
> > infinitely many nodes (bits).
> And yet you claim that no node is infinitely far from the root? Wrong.

When you can produce a mathematically valid proof that adding 1 to a
finite number will produce an infinite number, you may claim that there
are nodes infinitely far from the root node, but until then, it is you
who are worng
.



Relevant Pages

  • 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)
  • Re: abundance of irrationals!)
    ... A maximal path is one which starts at the root ... >>> path contains an infinite sequence of branches. ... > tree is by a finite sequence of braches and nodes. ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... >>> connections, in which case that is also specified by the string of digits ... A maximal path is one which starts at the root ... >> path contains an infinite sequence of branches. ... > You have infinite maximal paths, with branches infinitely far from the root ...
    (sci.math)