Re: Cantor Confusion


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.


[The terms "constructable" and "computable" do not mean
the same thing. The word you want is "computable"]

With the definitions you use, the set of computable numbers
is not countable.

- William Hughes

.