Re: how

On 4/12/24 10:40 AM, WM wrote:

Le 12/04/2024 à 16:02, Richard Damon a écrit :

On 4/12/24 9:45 AM, WM wrote:

 

There are no "Natural Numbers" with less than ℵo successors.

 Self-contradiction: These successors are natural numbers but can't be used because they can't be used up.

Nope, because every successor to a Natural Number has, itself ℵo successors.
Yes, you can't "Use Up" the Natural Numbers with finite operations, but they can all be "Used".
Why do you think we can't use any of the Natural Numbers as part of the ℵo successors for that number?
Your "Set of number with less than ℵo successors" is just an empty set, so you set of numbers that show the problem is empty, so no problem detected.

 Regards, WM