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

On 12/12/24 9:25 AM, WM wrote:

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
 

But a segment that is infinite in length is, by definiton, missing at least on end.
That end isn't "infinite", it doesn't have an end in that direction.
You might notionally call that end "infinity", but that isn't its end, and it would be an "open" end for that segment (as infinity isn't a finite number, so isn't an element of any segment of finite numbers).
So, all you are doing is showng that you don't understand what you are talking about, and just making up shit to try to sound like you do.
This just show why your logic has blown itself up into smithereens from its contradictions, since you can't follow the definitions of real math.
So, which bijection from Cantor are you talking about? Of are you working on a straw man that Cantor never talked about?