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

On 1/12/25 2:39 PM, WM wrote:

On 12.01.2025 20:33, Jim Burns wrote:

On 1/12/2025 10:54 AM, WM wrote:

 

No, it depends on completeness.

>
It is completely true
that each natural number is a natural number   and
that only natural numbers are natural numbers.

 and that nothing fits between them and ω.

ℕ is the set of finite ordinals.

 such than none can be added.
 Regular distances in (0, ω) multiplied by 2 remain regular distances in (0, 2ω).
 Regards, WM
 

No it would be the regualar distances in (0, omega), since you excluded omega from the set/interval, and thus is is nothing but the basic infinite set, when when doubled is exactly the same length, infinite.
Your problem is you thing that omega-1 is a thing in the number system you are talking about, but it isn't.