Re: Cantor Confusion

In article <1161159675.931671.301310@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:

In article <1161008572.469763.93200@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
mueckenh@xxxxxxxxxxxxxxxxx writes:
> jpalecek@xxxxxx schrieb:
...
> > The fact that you cannot compute a list of all computable reals does
> > not mean that there is no list of all computable numbers. There is
> > one,
> > and it is not computable.
> >
> The fact that you cannot compute a list of all reals does not mean that
> there is no list of all reals. There is one, but it is not possible to
> publish this list.

You are seriously wrong.

You should have noted that this was an ironic reply. But in order to
avoid machines and undecidabilities:
The set of constructible numbers is countable. Any diagonal number is a
constructed and hence constructible number.

No nth-listed number needs to be "completely" constructed, but only
constructed far enough to determine its nth digit, so that no number in
the listing needs to be constructible, nor does the set of listable
numbers need to be a subset of the set of constructible numbers.

Every list of reals can be shown incomplete in exactly the same way as
every list of contructible reals can be shown incomplete.

But as the lists need not be restricted to constructible numbers in
order to allow construction of a diagonal different from all of them,
that argument does not hold.

Regards, WM
.

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