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

Yes,
if each end.segment is infinite
then each end.segment is infinite.

 

because all are
predecessors of an infinite endsegment.

 

That means it is valid for all endsegments.
>
The trick here is that
the infinite set has no specified natural number (because all fall out at some endsegment)

 all fall out == empty

 

but it is infinite

 infinite and empty