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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted: Jan 11, 2013 4:14 AM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 10 Jan., 23:04, Virgil <vir...@ligriv.com> wrote:
>

> > What he, and I, find incomprehensible is why
> >    "the anti-diagonal can at no finite position
> >     deviate from every entry of the list"
> > is presumed to imply
> >    "That means it can never deviate from every entry."

>
> At no finite position means never because there are no infinite
> positions, in mathematics.

But the antidiagonal CAN deviated from each entry of the list at a
position unique to that entry, since it has as many positions in it as
there are entries to deviate from.
> >
> > What prevents the diagonal from differing from entry n at position n,
> > and thus differing from each entry?

>
> Position n is a finite position. But it is clear that for every finite
> position there is a double of the diagonal.

That appears to be saying that the entire diagonal appears in one or
more finite positions.

It is much more clear that for every entry there is a finite position at
which the diagonal differs from it.

If fact the nth entry differs from the diagonal at its nth position, in
addition to any other positions at which it may, but need not, differ.

Thus for every n in N, the nth entry differs from the diagonal in AT
LEAST the nth place.

That WM deliberately blinds himself to the obvious does not make it any
less obvious to those who do not deliberately blind themselves to it.

And unless WM can give an explicit rule for determining WHICH entry the
diaganal does not differ from, his claim is invalid outside WMytheology.
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