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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Thu, 6 Mar 2025 18:15:01 +0100
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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.

>>
>> Induction is potentially infinite.
> 
> Proof.by.induction completes

never!

Regards, WM