Re: abundance of irrationals!)

aeo6 Tony Orlow wrote:
> Russell said:
> > aeo6 Tony Orlow wrote:
> > > Russell said:
> > > > aeo6 Tony Orlow wrote:
> > > >
> > > > [snip]
> > > >
> > > > > Excuse me, but the nodes of an infinitely deep binary tree
can
> > > > obviously be
> > > > > enumerated in a linear manner, corresponding to binary
integers
> > and
> > > > thus to the
> > > > > naturals.
> > > >
> > > > Yes.
> > > >
> > > > If you want to complain that it would require infinite digits
for
> > > > > most values,
> > > >
> > > > Huh? What does that even mean? What values are you
> > > > talking about? And digits of what?
> > > Duh. The digits of the binary number that represent each node on
the
> > tree,
> >
> > Ok; if that's what you mean, then each node on the tree
> > is represented by a *finite* sequence of digits.
> The tree has infinitely long branches, so no, you're wrong.

Well, this is the essence of our disagreement, and if
we can't get this basic thing cleared up then there's no
point in my going further with the discussion.

Now, I haven't been following this thread, so I don't
know what your position is on the following question: Do
you believe there is some natural number with infinitely
many digits? If you don't, then there is some hope, but
otherwise, i.e. if you do, I think I will bow out as there
cannot be anything for me to add to the discussion that has
not already been said.

[snip]

.

Relevant Pages

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    ... A branch defines one of those digits, and a path is a string of ... >> which is implemented in a binary tree as a path, ... > the naturals are represented, ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... >>> each of these two paths is the root of another maximal binary tree, ... > If we call the set of all paths continuing a particular node the "bunch" ... >>> How does one write down an infinite digit? ... >> discussed the correlation between the paths aand strings of digits. ...
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  • Re: Cantor and the binary tree
    ... >> each of these two paths is the root of another maximal binary tree, ... there extend two dependent branches reaching two more nodes, ... > An infinite number of digits, ... > discussed the correlation between the paths aand strings of digits. ...
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