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

On 17.11.2024 13:28, Mikko wrote:

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.

 There are 100 intervals for each natural number.
This can be proven by bijecting J'(100n) and J(n). My intervals are then exhausted, yours are not.

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.

 Only if you believe in matheology and resist mathematics.

Geometry says that your intervals cover the real line, my do not.