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

On 1/8/2025 9:35 AM, WM wrote:

On 08.01.2025 12:04, FromTheRafters wrote:

WM formulated on Wednesday :

If ω exists, then ω-1 exists.

>
Wrong.

>
A set like ℕ has a fixed number of elements.

Yes.
Our sets do not change.
Our set ℕ does not change.

If ω-1 does not exist,
what is the fixed border of existence?

Membership in ℕ is determined by ℕ.rule.compliance,
not by position relative to a border.element.
Each object complying with the ℕ.rule is in ℕ
Each object not.complying is not.in ℕ
Compliance and non-compliance do not change.
Membership does not change.
No element is the border.element
because
each element is smaller.than another, fuller element,
and so, not on the border.
Which elements are in ℕ doesn't change.