Re: The set of necessary FISONs

On 3/1/25 7:46 AM, WM wrote:

On 28.02.2025 18:26, joes wrote:

Am Fri, 28 Feb 2025 17:44:17 +0100 schrieb WM:

On 28.02.2025 15:46, Richard Damon wrote:

 

Yes, at any finite point in the iteration, the set build so far has a
maximum element, but when we let the process complete (even though we
can't do it) the result changes to not have a maximum element.

The process cannot be completed with FISONs. Each one is finite, and so
is their potentially infinite number. That does never change.

Yes, it can.

 Try it! By induction?
 Regards, WM
 

FISON(1) exist as { 1 }
if FISON(n) exists as { 1, 2, 3, 4, ... n } then FISON(n+1) exists as FISON(n) Union {n+1}
Therefore, by induction, there exists an infinite set of FISONs FISON(n) for ALL values of n in the set of Natural Numbers.
Note, just like every natural number is finite, but the set of them is infinite, we have that every FISON is fininte, but the set of all of them is infinite.
Your claim that we can't complete the process just says your logic doesn't accept the axiox of inducition, and thus you don't actualy have the Natural Numbers.