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

On 2024-11-17 10:29:31 +0000, WM said:

Your J'(n) = (n/100 - 1/10, n/100 + 1/10) are 100 times more than mine.
For every reordering of a finite subset of my intervals J(n) the relative covering remains constant, namely 1/5.
The analytical limit proves that the constant sequence 1/5, 1/5, 1/5, ... has limit 1/5. This is the relative covering of the infinite set and of every reordering.

My J'(n) are your J(n) translated much as your translated J(n) except
that they are not re-ordered.
My J'(n) are as numerous as your J(n): there is one of each for every
natural number n.
Each my J'(n) has the same size as your corresponding J(n): 1/5.
One more similarity is that neither is relevant to the subject.
--
Mikko