Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/27/24 2:15 PM, WM wrote:

On 27.11.2024 18:58, Richard Damon wrote:

On 11/27/24 12:13 PM, WM wrote:

 

Replacing every element of the set {0, 1, 2, 3, ...} by its successor yields {1, 2, 3, ..., ω}. The number of ordinals remains the same, the number of finite ordinals decreases.

>
Nope, because omega is NOT the successor for any natural number, the successor of EVERY Natural Number is a Natural Number.

 The successor of the last natural number is ω.

But there isn't a last natural number, if there was, there would only be a finite number of them.
That is what breaks your logic, you just can't handle the infinite.

 

It it the successor for the SET of natural numbers.

 And that is nothing else but all natural numbers.

No, the set is different from its members.
OI guess you logic is based on the proven inconsistant naive set theory which is why it gets so must worng.

 Regards, WM