Re: The set of necessary FISONs

On 3/1/25 6:58 AM, WM wrote:

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.
 REgards, WM
 

But what is "n" in the above definition?
That you can't talk about that, shows your definition is incomplete.
Note, the value AT the limit, and the values appraching the limit of things can be different.
And, that disappearance of the infininte above each n is one of those things,
You are just showing that you don't understand what you are talking about, and are stuck with assumptions that only work in finite systems, that blow up your logic when you move to the infinite.
It is a very basic fact that as we broaden into higher orders of the infinite, some of the properties of the finite or lower orders no longer apply, and to assume they do breaks your system.
That fact that you are stuck in a Naive Logic system using Naive Mathematics says that you just can't bridge to infinity, as it breaks your Naive assumptions.