In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 21 Mrz., 04:06, Virgil <vir...@ligriv.com> wrote: > > > For any natural n in |N, we can know that n lines fail, but we can also > > know that any infinite set of lines succeeds. > > No. You are so blinded by what you have learned that you think you > knew that. But if you applied induction to the set M of unnecessary > lines, you could find the contrary.
While induction can certainly prove that no finite set of lines is sufficient, it cannot prove that an infinite set of lines cannot be sufficient, because some infinite sets of lines clearly ARE sufficient, the set of all lines, for example, is both infinite and sufficient.
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 so frequently with things mathematical, wrong. --