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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 2 Mar 2025 19:05:12 +0100
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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?
>>
>> 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