Date: Jan 16, 2013 7:21 PM
Subject: Re: WMatheology � 191
WM <firstname.lastname@example.org> wrote:
> 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.
My "assertion" is that for each n in |N, the antidiagonal differs from
string n in place n.
AS as the antidiagonal differing from a string in one place means that
the antidiagonal differs from that string, we have that the antidagonal
differs from EVERY string in al least one place per string, which is all
that is needed
> > So there is nowhere in the list that can occur without differing from
> > an antidiagoal.
> Tell me the n which allows you to consider your check as completed.
What makes you think there is a "last" one, when all of them are done?
> > > 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.
Since I cannot know which ones you used until you tell me, and you
refuse to tell me, why should I be able to tell you until you tell me?
> But you cannot.
Only because you will not tell me which ones you used.
Given any finite or countably infinite list of binary lists, it is
possible to identify a non=member.
WM's refusal to give such a list tells me that he does not have one
which does what he claims for it.