Re: The set of necessary FISONs

On 2/23/25 5:04 AM, WM wrote:

On 22.02.2025 19:21, joes wrote:

Am Sat, 22 Feb 2025 19:02:12 +0100 schrieb WM:

 

If every FISON can be omitted, then nothing remains for a sufficient set.
Because if there was any sufficient set, it would have a first FISON.

Haven't you agreed that omitting everything does change the union?

 Omitting everything does change the real union but not the assumed union.
 Regards, WM
 

But not the set that you imply is desired, a set of FISONs whose union becomes the Natural Numbers.
Since *ANY* infinite set of FISONs will acheive that, your end results is proven wrong, because the fact that no FISON is in a set a FISON that must be in that set exist (and thus the set of REQUIRED FISONs is empty).
You are just confusing "Required" / "Necessary", with "Sufficient".
Just like you always confuse things.