```Date: Jan 12, 2013 5:03 PM
Author: Virgil
Subject: Re: Matheology � 191

In article <40a214e5-f8d0-4670-8218-5b49711eff9d@f4g2000yqh.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> 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--
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