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

On 12.12.2024 13:26, Richard Damon wrote:

On 12/12/24 4:12 AM, WM wrote:

Note, "inifinite" isn't a Natural Number,

But a state,often dscribed byan infinite whole number.

or a Real Number, so NO segement, specified by values, can have an "infinte endsegment".

Every infinite segment is an infinite segment and therefore has an infinite segment as subset. But if Cantor can apply all natural numbers as indices for his bijections, then all must leave the sequence of endsegments. Then the sequence (E(k)) must end up empty. And there must be a continuous staircase from E(k) to the empty set.
Regards, WM