On Jan 12, 11:56 am, 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... >
No it cannot be constructed in that manner, simply because it would no longer be a BINARY tree. > 0 > 1, 2 > 3, 4, 5, 6 > 7, ... > > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths. >
The complete Binary tree contains 2^aleph_0 paths and 2^aleph_0 paths is strictly greater than aleph_0, this is pretty much standard stuff that most mathematicians actually all leading mathematicians of the last century and this one hold to be true.
> 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. > > 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? > > Regards, WM