Date: Jan 12, 2013 5:03 PM
Subject: Re: Matheology � 191
WM <firstname.lastname@example.org> wrote:
> On 12 Jan., 16:57, David C. Ullrich <ullr...@math.okstate.edu> wrote:
> > On Sat, 12 Jan 2013 00:56:10 -0800 (PST), WM
> > <mueck...@rz.fh-augsburg.de> wrote:
> > >Matheology 191
> > >The complete infinite Binary Tree can be constructed by first
> > >constructing all aleph_0 finite paths and then appending to each path
> > >all aleph_0 finiteley definable tails from 000... to 111...
> > > 0
> > > 1, 2
> > > 3, 4, 5, 6
> > >7, ...
> > >This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.
> > >If there were further discernible paths, someone should be able to
> > >discern one of them. But since all possible combinations of nodes
> > >(including all possible diagonals and anti-diagonals of possible
> > >Cantor-lists) that can occur in the mathematical discourse already are
> > >present, a human being cannot discern anything additional.
> > So far no reason to comment. The same errors as always, paths
> > are not all finite,
> Yes, same misunderstandings as always. I described exclusively
> infinite paths. But nobody can describe them bit by bit. So I use
> finite initial segments and appended infinite tails. Have you
> generally difficulties to understand written texts?
He has a good deal less such difficulty that WM has.
> > existence is not the same as being "discernible",
> > etc.
> You are invited to "discern" another path from the countable bunch of
> infinite paths that I used to construct the Binary Tree.
Until you list the ones that you used, there is no way to "discern"
another, but any list you provide also provides a nonmember.
> > >Matheologians may claim that God can discern more. But God is not
> > >present in mathematics. Mathematicians have no pipeline to God, as
> > >Brouwer put it. At least God does never reveal mathematical secrets.
> > >Or has any reader ever heard God tell a mathematical secret?
> > But this is new, at least as far as I recall! Are you familiar with
> > the word "straw man"? When has a mathematician invoked
> > God as part of the proof that the set of paths is uncountable?
> You seem not very familiar wíth the relevant literature. Cantor took
> God as his witness that there are all numbers. He quoted St. Augustin
> that God knows all natural numbers in order to prove that they exist.
> Cantor was convinced that the set of angels is infinite. Cantor used
> the holy Bible to prove that God rules beyond the first infinity. The
> infamous listener of Brouwer's famous talk at Göttingen claimed that
> God knows the complete decimal representation of pi. And finally you
> should know that it is impossible for men to have a list of all reals,
> That mans nobody can learn, know, or quote all reals. If they should
> exist, only God can know them.
One reason that no man can have a list of all reals is that any such
list provides the proof of its own incompleteness.
> Regards, WM