On 18 Jun., 20:32, Virgil <virg...@nowhere.com> wrote: > In article > <85db7468-1f62-407e-8232-aa31838b5...@o20g2000vbh.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 17 Jun., 21:20, William Hughes <wpihug...@hotmail.com> wrote: > > > > > Why should the subset belong to one element of the list of > > > > paths > > > > It doesn't. > > > "the tree contains a subset of nodes that is > > > *not* contained in one element of the list of paths" > > > As it is neither contained in a path of the tree, this observation is > > completely irrelevant. > > If the original list of paths is no more than countable and the tree is > a maxima; infinite binary tree, then there are necessarily paths in that > tree not in the list. > This is so because countably many paths can cover all nodes but cannot > cover all paths
but they do, nevertheless
> as Cantor proved.
Therefore he was wrong.
During the next 100 years we will laugh about his giant joke - and then he will be forgotten by mathematicians, except by some historians.