Date: Jan 16, 2013 4:20 PM
Subject: Re: WMatheology § 191
On 16 Jan., 20:16, Virgil <vir...@ligriv.com> wrote:
> > > > Your string can and will differ from the nth string. But there will
> > > > always an identical string be in the list
> > > Identical to what?
> > Identical to every initial segment of the anti-diagonal.
> If that alleged "identical string" were in some position n in the list
> then it will differ from any anti-diagonal at its own position n.
There are infinitely many positions following upon every n. So if your
assertion is true for every n, then there are infinitely many
remaining for which it is not true. This holds for every n.
> So there is nowhere in the list that t can occur without differing from
> an antidiagoal.
Tell me the n which allows you to consider your check as completed.
> > And the handwaving claim to "differ in the infinite"
> > can be rejected by stating that in mathematics there is no chance to
> > differ in the infinite.
> That not being what is claimed for a true Complete Infinite Binary Tree,
> it is an irrelevancy.
> What is claimed, and what is true, is that any two distinct paths in a
> CIBT differ at infinitely many finite levels, i.e., will have only a
> finite initial sequence of nodes in common, and not have any other of
> their infinitely many nodes in common.
Then you should be able to identify and distinguish by nodes one of
the asserted uncountably many paths from all countably many paths that
I used to construct the Binary Tree.
But you cannot.