Virgil
Posts:
4,479
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 5:02 PM
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In article
<6f0337ce-7dee-4af5-af99-99e55f7ce7fb@d4g2000vbw.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.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.
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