Re: The set of necessary FISONs

Am Sat, 01 Mar 2025 15:40:45 +0100 schrieb WM:

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.

It does, that is why you take the limit.

A limit exists if every
difference can be undercut. Here the difference remains infinite.

Yet larger numbers are closer.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.