In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 14 Mrz., 19:52, fom <fomJ...@nyms.net> wrote: > > On 3/14/2013 5:52 AM, WM wrote: > > > >> A particular claim must be made before Cantor's argument > > >> can even apply. > > > > >> That particular claim is that there is a single infinity > > >> that is referred to in language as an object. > > > > > No. That particular claim is that infinity can be complete > > > > Wrong. The completeness issue is entirely separate > > from the diagonal proof. > > Cantor's opinion about his proof is wrong?
WM's misrepreetataion of it is the thing that is wrong, just like his misrepresentation of a simple bijection as being a homomorphism of linear spaces. > > > > It is clear that you completely fail to understand > > that. > > Cantor failed to understand his proof too?
No, Only WM misundertands it.
> Of course you may be better than he, or you may at least think so.
We all do better than thee! > > > Whether this is because your general feelings > > concerning infinity make you unable to see the difference > > or simply because you are pursuing an agenda makes > > no difference. > > It is because I have read and understood Cantor's arguments.
Another self-delusion surfaces! > > > > In the Grundlagen (or, at least in the translations which > > my ignorance forces me to use), Cantor explains in > > detail why the logical construction of real numbers > > from sets of rationals is reasonable and how one should > > think about accepting the construction as legitimate. > > Then you should also read his thoughts about infinity.
Reading without understanding, as WM so often does, does not help. > > > > Nor can one attribute the completeness issue to Cantor > > alone since Dedekind was addressing the same issue > > differently. > > Dedekind got his idea of infinity from Bolzano. I think that I think > that I think ...
WM may think that he thinks, but he is wrong.
> That is never finished. Zermelo got his idea of infinity (his axiom) > from Dedekind, but inadvertently changed its meaning to actuality, > because that is required for Cantor: There is a set, that means there > are all elements of the set. > > > > You would be correct to say that Cantor believed in > > a completed infinity so that the diagonal argument > > motivated his further researches. But, you need > > to differentiate what the proof does and how it > > does it from other mathematics that involves > > completed infinities > > It is so simple: > If the list is only potentially infinite, then it is not possible to > decide whether a number can be excluded definitively. But it is > necessary for Cantor's argument to exclude the diagonal from the whole > list - not only from the first n lines for every n, because after > every n there follow infinitely many more. It is not possible to judge > about the complete list because incomplete infinity is incomplete. Is > that so difficult to understand?
What Cantor proved was that the existence of an infinite list of binary sequences proves its own incompleteness, thus no complete infinite list of binary sequences can exist:
THEOREM: IF there is a countable list of binary sequences, THEN that list is incomplete.
PROOF: GIVEN such a list, one can define from it a binary sequnce not in it.
The only way for Cantor's theorem to be false would require the existence of a complete infinite list.
So that in WMytheology, such a complete infinite binary list must exist. > > > Here it is again. Think about it: > It is not possible in potential infinity to judge about the complete > list because incomplete infinity is incomplete.
Then it follows that the hyporthesis is false and theorem is true!
WM has frequently claimed that a 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 must first show that the set of all binary sequences is a vector space and that the set of paths of a CIBT is also a vector space, which he has not done and apparently cannot do, and then show that his mapping satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of a field of scalars and x and y are f(x) and f(y) are vectors in suitable linear spaces.
By the way, WM, what are a, b, ax, by and ax+by when x and y are binary sequences?
If a = 1/3 and x is binary sequence, what is ax ? and if f(x) is a path in a CIBT, what is af(x)?
Until these and a few other issues are settled, WM will still have failed to justify his claim of a LINEAR mapping from the set (but not yet proved to be vector space) of binary sequences to the set (but not yet proved to be vector space) of paths ln a CIBT.
Just another of WM's many wild claims of what goes on in his WMytheology that he cannot back up. --