Virgil
Posts:
8,833
Registered:
1/6/11


Re: ZFC is inconsistent
Posted:
Mar 17, 2013 3:36 PM


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 nonexistence > > 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.
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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.
But frequently claims already to have done it. 

