Re: The set of necessary FISONs

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!