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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 1 Mar 2025 15:40:45 +0100
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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