Re: Two results of set geometry

On 31 Aug., 04:18, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1188495397.998255.260...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueck...@xxxxxxxxxxxxxxxxx> writes:
...
> But in order to shorten the discussion: It is impossible to
> define or construct a bijection between the set of constructible reals
> and N.

Again you are guilty of abuse of terminology. Using common mathematical
terminology, it is possible to construct a bijection between N and the
constructible numbers. I even gave the construction in an article in
response to your garbage.

I did not see it. (By the way, do I have the point?) But if you can,
then define it and take the diagonal number which then is defined too.

But you mean "finitely defined". State so
when you mean that. And be aware that that notion holds a lot of
problems.

Perhaps there are problems in matheology but not in mathematics. Any
number which can be defined, i.e., which can be addressed as an
individuum, is a finitely definable number. (Becausen non-finite
definitions are not definitions.)

It is sufficient when you show an *injection* between the paths and N.

Every separation requires a node. There cannot be more separated paths
than nodes. The bijection between nodes and natural numbers is
obvious. So what do you not understand?

Regards, WM

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