In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote: > > > > In fact? That's amazing. So we cannot prove that all lines of the > > > infinite set of lines are unnecessary? > > > > We can prove that something is true for every > > member of an infinite set. We cannot > > prove that something is true for the set > > itself unless the set is finite. > > But I am not interested in the set itself. Not at all! My claim is > that every member of the set of lines can be removed such that no > member remains, but every natural number is contained in the list. > > Do you agree?
Outside of Wolkenmuekenheim, a list of lines with no lines in it is the empty set.
Only in Wolkenmuekenheim can an empty set contain anything at all.
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. --