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

On 2024-12-15 11:25:26 +0000, WM said:

On 15.12.2024 11:56, Mikko wrote:

On 2024-12-14 08:53:19 +0000, WM said:

 

Please refer to the simplest example I gave you on 2024-11-27:
The possibility of a bijection between the sets ℕ = {1, 2, 3, ...} and D = {10n | n ∈ ℕ} is contradicted because for every interval (0, n] the relative covering is not more than 1/10, and there are no further numbers 10n beyond all natural numbers n.

 It is already proven that there is such bijection. What is proven cannot
be contradicted unless you can prove that 1 = 2.

 What is proven under false (self-contradictory) premises can be shown to be false.

If your premises are contradictory (as they seem to be) then everything
can be proven to be both true and false.

Here we have a limit of 1/10 from analysis and a limit of 0 from set theory. That shows that if set theory is right, we have
1/10 = 0 ==> 1 = 0 ==> 2 = 1.

That is the fallacy of equivocation. The limit of analysis is a different
concept from the limit of set theory.
--
Mikko