Re: The set of necessary FISONs

On 3/1/25 9:40 AM, WM wrote:

On 01.03.2025 14:26, joes wrote:

Am Sat, 01 Mar 2025 12:58:28 +0100 schrieb WM:

On 28.02.2025 18:25, joes wrote:

Am Fri, 28 Feb 2025 18:04:33 +0100 schrieb WM:

>

Zermelo doesn't say that Z is in Z.

But he says that the infinite Z exists because of his induction.
>

Therefore we use FISONs without approaching ℕ.

They do reach N in the limit.

No. ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo. Note for all! The limit
cannot exist without bridging this infinite gap.

Taking a limit "bridges the gap".

 No, not for infinitely many missing numbers. A limit exists if every difference can be undercut. Here the difference remains infinite.
 Regards, WM
 

But can be undercut with an infinite operation, that of "completing" the limit.
Your problem is you logic doesn't allow for infinite operations, and thus can not handle the infinite sets created by them, and it blows itself (and your intelegence) when you try to use them there,