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

On 1/9/2025 1:25 PM, WM wrote:

On 09.01.2025 18:52, Jim Burns wrote:

On 1/8/2025 9:31 AM, WM wrote:

(Losing all numbers but
keeping infinitely many
can only be possible if
new numbers are acquired.)

>
No.

>
Losing all numbers but keeping infinitely many
is impossible in inclusion-monotonic sequences.
>

Sets do not change.

>
But the terms (E(n))
differ from their successors by one number.

Each end.segment is larger than
any ordinal smaller.than fuller.by.one sets.
ℕ is the set of such ordinals.
End.segment.successors are
emptier.by.one but not.smaller.by.one.

Not all sets are finite.
⎛ By 'finite', I mean
⎝ 'smaller.than fuller.by.one sets'

>
Spare your gobbledegook.
Finite means like a natural number.

...which doesn't define 'natural number'.
Do you (WM) disagree with
'finite' meaning
'smaller.than fuller.by.one sets'?