Re: The set of necessary FISONs

On 2/14/25 7:46 AM, WM wrote:

On 13.02.2025 15:02, joes wrote:

Am Thu, 13 Feb 2025 14:51:44 +0100 schrieb WM:

On 13.02.2025 13:54, joes wrote:

Am Thu, 13 Feb 2025 12:59:56 +0100 schrieb WM:

>

All of us who know induction know that by induction we have obtained
that all FISONs can be removed without changing the result.

The result has certainly changed from a nonempty set, whatever you
think the union of inf. many FISONs is.

The assumption was UF = ℕ and has not changed by omitting any FISON.

Yes, but it does change when you omit *all*.

 It does because induction is valid for all elements of the inductive set.
 

UF is not empty.

 When will you learn that nobody claims such a nonsense?
 Regards, WM

But you need to remember what set you are doing induction on.
Your are BUILDING the set of "Not individually needed" FISONs, not the set of FISONs you can use to take a union of to make the Natural Numbers.
That last set, the way you are trying to define it, is only a set in Naive Set Theory, and thus part of a broken logic system.
The emptyness of the set of FISONs that are individually required doesn't elimiate them from the set of FISONs you can union to make the Natural Numbers.
Not unless you agree that your logic says 36 can't be factored.
Sorry, you are just proving your stupidity,