Virgil
Posts:
9,012
Registered:
1/6/11


Re: Matheology � 233
Posted:
Mar 30, 2013 8:56 PM


In article <2bc13fff5cbb43dda06a218c68c99849@m9g2000vbc.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.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 antidiagonal? Yes or no?
Lists and trees are different. And antidiagonals 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. 

