In article <email@example.com>, 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 --