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Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Posted:
Jan 10, 2013 6:11 AM
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On Jan 10, 12:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> So stop your clumsy handwaving and try to recover.
>
YOU try to Recover from your nonsensical misinterpretations.
> Try again: Consider the list of all terminating decimal
> representations.
> For every n we have:
> The anti-diagonal up to line n must be different from every entry up
> to line n.
Nonsense, that is YOUR misinterpretation of Cantor's arguments. This
is obviously FALSE, and Cantor never said something like that or
anything that can lead to such ridiculous result.
> The anti-diagonal up to digit n must have a double up to digit n.
Of course, because the list is defined as the list of ALL terminating
decimal representations. That is correct and natural and Cantor's
arguments Agrees with that completely.
> Result: The diagonal cannot be an entry of the list.
Oh really, I'm amazed, are you serious? of course the diagonal is NOT
an entry of the list, this is a silly remark on your behalf, the list
ONLY contains TERMINATING decimal representations, while the diagonal
and the anti-diagonal are non terminating decimal representations so
of course they are not on the list, ARE you thinking well?
> The diagonal cannot be different (at a finite position) from all
> entries of the list (and elesewhere, after all finite positions, it
> cannot be anything at all).
> This is a contradiction.
Where is the contradiction? Everyone knows the TRIVIALITIES you are
speaking about, of course the diagonal and the anti-diagonal cannot be
different (at a finite position) from all entries of the list, because
the list is of ALL finite initial segments of reals, Cantor agrees to
that, and every result based on Cantor's argument is consistent with
that. The contradiction only lies in YOUR head, you thought that
Cantor is saying something against that, which neither he nor anyone
who is sane have objected to that or have presented any line of
reasoning that contradicts that. You are just fighting your own
misinterpretations of Cantor, and blaming Cantor for your own
misinterpretations. WAKE UP!
>
> Regards, WM
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