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

On 13.12.2024 20:00, Jim Burns wrote:

On 12/13/2024 6:25 AM, WM wrote:
>
Each finite.cardinal
⎛ is first in an end.segment.
⎝ is used as a index of an end.segment.
 Each finite.cardinal
⎛ is absent from an end segment.
⎝ is emptied from the end.segments.

If endegments were defined as E(n) = {n+1, n+2, ...}:
E(0) = {1, 2, 3, ...}
E(1) = {2, 3, 4, ...}
E(2) = {3, 4, 5, ...}
...
E(ω-1} = { }.
Then this change from content to index would even be more obvious.

(ℕ to the set of endsegments, ℕ to ℚ,
ℕ to the lines of the Cantor list
for "proving" the uncountability of ℝ)
shows inconsistency.

Each set has
its emptier.by.one and fuller.by.one counterparts.

If all natnumbers can be used for mappings as indices then every natnumber has to leave the sequence of endsegments. Do you agree? Therefore their intersection is empty. Do you agree? Emptying by one only implies finite endsegment intersetcions. Do you agree? If not describe the process according to your opinion.
Regards, WM