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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