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.
> 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. 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.