In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote: > > > > But you think that after all finite and unnecessary lines another one > > > is lurking like a dragon? > > > > Now I think that after any finite set of unnecessary lines has > > been removed, there still remains an unnecessary line.- > > I know. That's what I wished to prove.
Considering WM's box score with proofs, don't anyone hold his breath.
> In order to believe in the > existence of actually infinite sets, it is necessary to have another > element after all ordinary elements have been removed.
Not outside Wolkenmuekenheim.
Given any infinite set of lines, it is still an infinite, thus sufficient set of lines to cover |N, after any finite set of lines have been removed from it, so that any finite subset of diminished but still infinite set is also a set of unnecessary lines.
WM claims to know how to map bijectively the set of infinite binary sequences, B, linearly to the set of reals and then map that image set of reals linearly ONTO the set of all paths, P, of a Complete Infinite Binary Tree.
But each binary rational in |R is necessarily the image of two sequences in B but that one rational can then only produce one image in P, so the mapping cannot be the bijection WM claims.
SO that WM is, as usual with things mathematical, wrong. --