Virgil
Posts:
6,970
Registered:
1/6/11


Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 5:02 PM


In article <6f0337ce7dee4af5af9999e55f7ce7fb@d4g2000vbw.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 3 Jan., 17:30, Zuhair <zaljo...@gmail.com> wrote: > > > > > I think that distinguishability in (2) is the same distinguishability > > in (1) it has exactly the same definition. > > Of course it is. To distinguish or not to distinguish, that is the > question. > > > > We have only COUNTABLY many finite initial segments of reals that we > > can distinguish of course on finite basis, that's what is available, > > we don't have more. > > And Cantor does not pretend to use more in his argument. So whether > there are indistinguishable reals is completely irrelevant for his > argument and the set of reals considered by him.
Thus you validate Cantor's diagonal argument regardless of whether ther are any indistinguishable reals at all. > > > By the way I might be wrong of course, I'll be glad to have anyone > > spot my error, > > You will not find anybody to do so. The matheologians only blather > irrelevant nonsense because it is obvious to every sober brain, that > Cantor was in error.
Except that a great many brains far more sober than WM's has ever been disagree with him on that issue.
That WM has a bee in his bonnet does not mean its buzzing need bother anyone else.
> But it seems to be so deeply inplanted in most > mathematicians brains that they are incapable of thinking the > opposite. I enjoy every semester the experience that 40 young and very > bright student understand immediately. Their only advantage is that > most of them never heard about Cantor until one week before I tell > them the truth. Poor sods may take years recovering from having WM's bees inserted into their bonnets.
It is a shame that the German Educational system allows such evils to occur. 

