Re: The set of necessary FISONs

On 2/1/25 7:24 AM, WM wrote:

On 31.01.2025 15:46, Richard Damon wrote:

On 1/31/25 5:21 AM, WM wrote:

 

 From this set O every finite subset can be subtracted without changing the result. Therefore,  by induction, no finite A(n) remains. Therefore the set O has no first ordinal. Therefore it is not a set of ordinals. Therefore your claim is wrong.

 

Induction doesn't work that way.

 It works that way: When n belongs to ℕ, then n+1 belongs to ℕ.
And it works also thos way:
When n can be deleted, then n+1 can be deleted. Nothing remains.

So, where was your "Induction".
Or, maybe you don't understand what induction actually is, since you don't understand logic.
But that is a nature consequence of

There is no requirement that a "minimal" set exists.

 There is the assumption that a set with U(A(n)) = ℕ exists. No element remains. The set does not exist.
 

But why do you make the assumption such a set exists? As I said, your logic also proves that we can't factor 36.

Regards, WM

Bad logic gives bad answers.
Insistance on bad logic proves stupidity.
Your logic, the assumption of a set of required FISONs, is the same logic that says that 36 can't be factored, so is bad.
All you are doing is proving your stupidity.