On 9 Jun., 18:34, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 9, 11:46 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > And uncountably many X through every node. > > Let us choose one of them and map it one that node. For the others we > > will find other nodes, below that one chosen. > > Nope. You cannot find enough other nodes. There are uncountably many > paths > going through the node and only countably many nodes below it.
That's just the proof saying why Cantor's proof is wrong! Cantor (and his disciples) assume that the complete diagonal of the famous list is the limit of an infinite process. But he and they deny that the complete binary tree is the limit of an infinite process. Cantor spelled that out in a letter to Letter to Vivanti of Dec. 3 1885: Introducing the expression "path" that Cantor did not use but mean, he said: "This apparent difficulty is solved as follows: The set of all "path" is not the limit of all "finite path" z_n for n = oo." This is an inconsistency. Either there is no limit at all (then Cantor's proof is wrong, because the list cannot be checked completely) or the limit holds also in case of the binary tree.