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

On 29.11.2024 16:16, Richard Damon wrote:

On 11/29/24 9:10 AM, WM wrote:

On 29.11.2024 14:57, Richard Damon wrote:

On 11/29/24 8:44 AM, WM wrote:

On 29.11.2024 01:06, Richard Damon wrote:

On 11/28/24 12:50 PM, WM wrote:

If for all intervals 1, 2, 3, ..., n the covering is 1/10, then there are no natnumbers outside of all intervals and there are no hats
outside of all intervals.

>

You are making the error of assuming that the infinite set is just like a finite set that has part of it.

>
No. Analysis concerns infinite sequences and sets.

>
You are looking at FINITE sets, and then trying to extrapolate to an infinte set, which doesn't work.

>
Analysis shows the way. If it differs from set theory, then one of both is wrong.
>

But set theory doesn't say anything that you are saying.

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.

 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.
Regards, WM