Re: The set of necessary FISONs

On 14.02.2025 13:52, joes wrote:

Am Fri, 14 Feb 2025 13:46:53 +0100 schrieb WM:

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.

„All”, i.e. inf. many, is not an element of that.

All are elements of the inductive set.

 

UF is not empty.

When will you learn that nobody claims such a nonsense?

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

All FISONs can be removed without changing the result.

That shows that UF = ℕ is wrong.
IF UF = ℕ THEN { } = ℕ.
Not Then UF = { }.
Regards, WM