Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 29.11.2024 19:56, Richard Damon wrote:

On 11/29/24 12:38 PM, WM wrote:

 

Set theory says that the sets ℕ = {1, 2, 3, ...} and D = {10n | n ∈ ℕ}
can be bijected by clever mapping. That means there are as many n as
10n as black hats. That means by clever shifting the black hats they
will cover all n.

Yep, that's what it says, and it is true.
Note, NOTHING in that statement talks about working with finite subset
of those sets,

That's why set theory is in contradiction with mathematics.

Nothing in set theory talks about the equivalence of properties of
the infinite set to the properties of the finite sets

That is the field of analysis. I believe that application of analysis
provides correct results for the infinite.

Apparently your concept of it doesn't, because you are using broken
rules,

No, I am using a very simple and sound rule. If all hats of finite
intervals (0, n] fail to cover more than 1/10,