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On 3/6/2025 4:15 AM, WM wrote: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.Am 06.03.2025 um 10:06 schrieb joes:Am Wed, 05 Mar 2025 22:05:04 +0100 schrieb WM:We do NOT construct[make] sets.Therefore iteration fails to produce>
actual infinity.
As an element, but not as
the number of elements (=the size of the set).
We construct[know] sets.
Never a set of elements is constructed which is larger than every finite number.The number of elements is an elementFor each element in a set which
for every element produced by induction.
is its.own.only.inductive.subset,
that element's set of priors has
fuller.by.one sets which are larger.
never!>Proof.by.induction completes
Induction is potentially infinite.
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