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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Thu, 6 Mar 2025 20:23:43 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Thu, 06 Mar 2025 18:15:01 +0100 schrieb WM:
> On 06.03.2025 14:47, Jim Burns wrote:
>> On 3/6/2025 4:15 AM, WM wrote:
>>> Am 06.03.2025 um 10:06 schrieb joes:
>>>> Am Wed, 05 Mar 2025 22:05:04 +0100 schrieb WM:
>> 
>>>>> Therefore iteration fails to produce actual infinity.
>>>> As an element, but not as the number of elements (=the size of the
>>>> set).
>> We do NOT construct[make] sets.
>> We construct[know] sets.
> Without their construction/proof we don't know whether infinite sets
> exist at all. Um aber die Existenz "unendlicher" Mengen zu sichern,
> bedürfen wir noch des folgenden ... Axioms. [Zermelo: Untersuchungen
> über die Grundlagen der Mengenlehre I, S. 266] The elements are defined
> by induction in order to guarantee the existence of infinite sets.
> 
>>> The number of elements is an element for every element produced by
>>> induction.
>> For each element in a set which is its.own.only.inductive.subset, that
>> element's set of priors has fuller.by.one sets which are larger.
> Never a set of elements is constructed which is larger than every finite
> number.
Infinite sets are.

>>> Induction is potentially infinite.
>> Proof.by.induction completes
> never!
If it didn't, it wouldn't work.

-- 
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.