On Apr 27, 3:12 pm, Virgil <vir...@ligriv.com> wrote: > In article > <7058d749-ce72-4a0e-9dd0-3d82f6554...@s4g2000vbr.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 27 Apr., 21:51, Virgil <vir...@ligriv.com> wrote: > > > > No one ever works with actual numbers in mathematics, > > > they only work with names or numerals for numbers. > > > Therefore no one can prove uncountability. > > If one had to get hold of actual numbers to do mathematics, there could > be no mathematics at all. > > And it is the axiom system for the field of real numbers which implies > uncountability, not the naming of numbers. > > > > > > So why is working only with names a problem? > > > That is not a problem in mathematics. It is a problem for > > matheologians. > > A type that exists only in WM's imagination, though he applies the term > broadly to the vast majority of those whom everyone else calls > mathematicians. > > > > > > > Infinite strings do not exist in the internet > > > > They do as named objects, as do numbers. > > > Yes, but not more than countably many. > > The evidence for uncountability does not rely on being able to name > uncountably many individuals. > > There are more things in heaven and earth, WM ,than are dreamt of in > your philosophy. > --
But, didn't you just dream of them in your philosophy? Or, is your theory incomplete, or inconsistent?
Having just put a name on all of them, congratulations: there's more. Basically Burali-Forti: Ord is irregular.
Well-order the reals, via Fefermann V = L, the universe as constructible has for each element: that's its own name. Are the reals a set?
The evidence for uncountability relies largely on constructive proofs. And, the arguments for uncountability of the reals don't apply to EF the natural/unit equivalency function.
Arguments for uncountability of the reals don't apply to EF: putting the elements of the unit interval in a row, while satisfying notions such as continuity, has range R_[0,1].
Bring forth applications of transfinite cardinals. EF has application as the unit line segment.