```Date: Mar 30, 2013 9:46 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 233

On Mar 30, 5:56 pm, Virgil <vir...@ligriv.com> wrote:> In article> <2bc13fff-5cbb-43dd-a06a-218c68c99...@m9g2000vbc.googlegroups.com>,>>>>>>>>>>  WM <mueck...@rz.fh-augsburg.de> wrote:> > On 30 Mrz., 22:11, Virgil <vir...@ligriv.com> wrote:>> > > > > Thus there is always at least one bit of any listed entry disagreeing> > > > > with the antidiagonanl, just as the Cantor proof requires.>> > > > In a list containing every rational: Is there always, i.e., up to> > > > every digit, an infinite set of paths identical with the anti-> > > > diagonal? Yes or no?>> > > The set of paths in any Complete Infinite Binary Tree which agree with> > > any particular path up to its nth node is equinumerous with the set of> > > all paths in the entire tree i.e., is uncountably infinite.>> > This was the question: In a list containing every rational: Is there> > always, i.e., up to every digit, an infinite set of paths identical> > with the anti-diagonal? Yes or no?>> Lists and trees are different. And anti-diagonals derive from lists, not> trees.> The entries in  list are well ordered.> The entries in a Complete Infinite Binary Tree are densely ordered.> Those order types are incompatible.> So questions, like WM's, which confuse them, are nonsense.> At least outside Wolkenmuekenheim.> --Zuhair simply brought forth an anti-diagonal argument for the infinitebalanced binary tree, and then the breadth-first traversal or sweepwas shown to iterate the paths that it didn't apply.With f = lim_d->oo n/d, n -> d, the elements of ran(f) are dense in[0,1] and well-ordered.Fuse the elements, or, un-fuse them:  don't con-fuse them.Regards,Ross Finlayson
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