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?
> 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.
> >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.