Re: The set of necessary FISONs

Am Sat, 01 Feb 2025 13:24:31 +0100 schrieb WM:

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.

It works this way: If n can be removed, n AND n+1 can be removed.
But it doesn’t work this way: „If n can be left out, all n can be.”

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.

The set of all segments is not empty.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.