Re: An uncountable countable set

In article <1155885445.248401.9340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:

*** T. Winter schrieb:

In article <1155725133.570350.44280@xxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> mike4ty4@xxxxxxxxx schrieb:
...
> The set of all constructible numbers including all real numbers in
> Cantor-lists and all of their diagonal numbers is countable.
> Nevertheless most people assert that the construction of a diagonal
> number would show the uncountability of this countable set of
> constructible numbers.

But can the list of constructable numbers be constructed?

No, of course it cannot, because only finite sets can be constructed,
at least if there is not a law connecting infinitely many numbers.

When talking with people, speak their language. I meant constructed
in a mathematial sense.

That they
are countable comes from other considerations.

It doesn't matter where that comes from. In fact all numbers which can
be constructed form a countable set.

Proof? And pray use the mathematical sense of constructed. Not what you
think it should mean.

(Unconstructible numbers were not at all taken into account
when Cantor's proof was published.)

Yes, right. Constructable numbers come from considerations in complexity
theory.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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