In article <zrudncWtmbvV7NjMnZ2dnUVZ_tGdnZ2d@giganews.com>, fom <fomJUNK@nyms.net> wrote:
> On 3/16/2013 4:55 PM, WM wrote: > > On 16 Mrz., 16:10, fom <fomJ...@nyms.net> wrote: > > > >> Borel was critical of the axiom of choice. > > > > Very. > >> > >> According to most accounts, it had been determined > >> that much of his work had implicitly used the > >> axiom of choice. > > > > There is no problem. The axiom of choice as such is completely > > acceptable. What is inacceptable (because provably false) is the > > application of AC to uncountable sets. This proves the non-existence > > of uncountable and actually infinite sets. > >> > >> Like you, he was critical of mathematics that he > >> used implicitly. > > > > No. > >> > >> In "Space and Time" Borel discusses the spatial > >> notion of sense. He points out that without > >> some sort of artifice one could not tell the > >> orientation of space. His example was the > >> sign of a determinant. I would suggest the > >> coloring of the vertices of tetrahedra. > >> > >> In other words, one must choose a labeling. > >> > >> You of course see only a finite process here. > >> > >> I see that you must fix points in space. > > > > No. A bar of 1 meter length is a single unit and can be coloured > > without any ideas about infinity. > > > Once again. You do not understand that > you invoke infinity when you purport > to refer to any part of an individual > as individual. > > I did not say 'color a tetrahedron'. > > When the four vertices of a tetrahedron > are given 4 colors, a second tetrahedron > can have its vertices given the same 4 > colors such that the two cannot be > superimposed. > > And the analytical orientation of a > space involves choosing a direction, > quadrant, octant, etc. preferentially. > > Prior to Frege and Cantor, mathematics > had no logic to make these distinctions.
And post WM, if he had his way, mathematics again would have no logic to make these distinctions.
WM has frequently claimed that HIS mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.
In order to show that such a mapping is a linear mapping, WM would first have to show that the set of all binary sequences is a linear space (which he has not done and apparently cannot do) and that the set of paths of a CIBT is also a vector space (which he also has not done and apparently cannot do) and then show that his mapping, say f, satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of the field of scalars and x and y and f(x) and f(y) are arbitrary members of suitable linear spaces.
While this is possible, and fairly trivial for a competent mathematician to do, WM has not yet been able to do it.