In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
That is the immediate result of a definition. That it may be produced as a limit is irrelevant.
> But he and they deny that the complete > binary tree is the limit of an infinite process.
The union of a set of infinitely many sets is a set regardless. And if infinitely many "complete" finite binary trees are regarded as sets of nodes, their union is a set of nodes in which every maximal totally ordered under "ancestor" set of nodes is a path and there are uncountably many such paths.
> 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
WM cannot claim Cantor is always wrong, as he so often does, and simultaneously cite him as an authority on what is right.