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

On 21.11.2024 16:39, Jim Burns wrote:

On 11/21/2024 5:21 AM, WM wrote:

That means the function describing this,
1/10, 1/10, 1/10, ...
has limit 1/10.
That is the quotient of
the infinity of black intervals and
the infinity of all intervals.

 The Paradox of the Discontinuous Function
(not a paradox):

It is a paradox that only 1/10 of the real line is covered for every finite interval (0, n] but all is covered completely in the limit. By what is it covered, after all n have been proved unable?

 lim.⟨ rc(1), rc(2), rc(3), ... ⟩  ≠
rc( lim.⟨ 1, 2, 3, ... ⟩ )
 You (WM) do not "believe in"
proper.superset.matching sets
discontinuous functions

There is no reason to believe in magic. But if you do, then all Cantor-bijections can fail as well "in the infinite". Then mathematics is insufficient to determine limits.
Regards, WM