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

On 21.11.2024 22:46, Jim Burns wrote:

On 11/21/2024 2:21 PM, WM wrote:

On 21.11.2024 19:54, Jim Burns wrote:

On 11/21/2024 11:24 AM, WM wrote:

 

By what is it covered,
after all n have been proved unable?

>
⎛ n ↦ i/j ↦ n
⎜
⎜ (i+j) := ⌈(2⋅n+¼)¹ᐟ²+½⌉
⎜ i := n-((i+j)-1)⋅((i+j)-2)/2
⎜ j := (i+j)-i
⎜
⎝ (i+j-1)⋅(i+j-2)/2+i = n

>
That is not an answer.

 You (WM) see it as "indistinguishable from magic".
That's a shame for your students.

To believe that the intervals can colour the real axis black is a shame for all members of humankind who do so.

The _description_ is completed.
It's right there.

The description of the set not of all its elements.
Either limits can be calculated from the finite, or not. If not, then Cantor's attempts are in vain from the scratch. If yes, then Cantor's attempts have been contradicted.
Regards, WM