Re: The set of necessary FISONs

On 02.03.2025 13:22, Richard Damon wrote:

On 3/1/25 1:18 PM, WM wrote:

On 01.03.2025 17:25, Richard Damon wrote:

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

>

∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo. Note for all! The limit cannot exist without bridging this infinite gap.
>

But what is "n" in the above definition?

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It is a natural number that we can represent in principle by making as many strokes.

 SO, Which Natural Number can it not be that makes N_def different than N?

They cannot be expressed, neither by stroks nor by digits. Their existence can only be proved: UF = ℕ ==> Ø = ℕ.

Note, the value AT the limit, and the values appraching the limit of things can be different.

>
The cannot differ by a fixed quantity like ℵo.

 Sure a limit can. What says it can't?

If it differes then it is not a limit by a matheologial credo in absurdum.
Regards, WM