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

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. Further it is only valid for the first numbers which are followed by almost all numbers. Never completed.

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.

 I am not enough of a scholar to know
that this is true of _all_ mathematics, but
I know that much knowledge of infinity,
including what I'm most familiar with,
is grounded in the _finite_

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.

 Here, I DON'T refer to finite numbers, etc.
I refer to finite sequences of CLAIMS,
each of which is true.or.not.first.false.

That is the sequence of claims that limits can be calculated from the finite and never the real axis is coloured black.
Regards, WM