Re: The set of necessary FISONs

On 12.02.2025 10:46, joes wrote:

Am Tue, 11 Feb 2025 20:23:28 +0100 schrieb WM:

On 11.02.2025 18:42, Jim Burns wrote:

On 2/11/2025 4:31 AM, WM wrote:

On 10.02.2025 16:16, Jim Burns wrote:

>

The set F of FISONs which can be removed without changing the assumed
result UF = ℕ is the infinite set F of all FISONs.

Yes.

Fine.

Actually, no: you can not remove the whole set, only single elements.

Induction proves all elements and even the set (Zermelo, Z).

The erroneous step is from „every finite number” to „an infinite number”.

Induction proves an infinite number.

Induction covers the whole infinite
set.

No, it only covers the elements.

All elements. None remains. Mithilfe der Definition über induktive Mengen lässt sich die Beweismethode der vollständigen Induktion rechtfertigen (daher auch der Name induktiv): Soll gezeigt werden, dass alle natürlichen Zahlen eine bestimmte Eigenschaft haben, so betrachte die Menge E ... [Wikipedia]

 

How induction works is not well known to you (WM).

What is wrong in my application in your opinion?

You incorrectly include infinity.

No, there is no infinite FISON. All are finite. All can be omitted without changing the result.
Regards, WM