Re: The set of necessary FISONs

On 1/28/25 4:56 AM, WM wrote:

On 28.01.2025 10:19, joes wrote:

Am Tue, 28 Jan 2025 09:58:14 +0100 schrieb WM:

On 27.01.2025 18:10, joes wrote:

Am Mon, 27 Jan 2025 15:33:01 +0100 schrieb WM:

>

Also an infinite set needs a first element.

No problem, any infinite set of FISONs has one.

But no set of FISONs the union of which is ℕ has a first element.

Yes it does. Any infinite set of FISONs has a first element.
>

But any set of FISONs fails.

No, any infinite set of FISON succeeds at having its union be the set N, what can't be done is pare that down to a "minimal" set, as the minimal set will still need to be countably infinite, and all countably infinite sets have the same "size" so none can be the "smallest"
You are just trying to use broken language, because you don't understand what you are talking about, and are too stupid to see your stupidity,

 

If an
infinite set was existing, you could easily find a first not completely
useless element.

No, as you have shown, no element is necessary.

 When every not necessary or not useful element has been discarded nothing remains.

But that operation can't be done, your logic removes one by one, and thus can't remove ALL.
All it shows is that you naive logic is broken,

 Regards, WM