Re: The set of necessary FISONs

On 2/26/25 6:59 AM, WM wrote:

On 26.02.2025 00:43, Richard Damon wrote:

On 2/25/25 9:18 AM, WM wrote:

 

Further I state that induction does not produce actual infinity.

>
Induction doesn't "Produce" anything, as you are using the wrong word.

 Um aber die Existenz "unendlicher" Mengen zu sichern, bedürfen wir noch des folgenden, seinem wesentlichen Inhalte von Herrn Dedekind herrührenden Axioms. ... Der Bereich enthält mindestens eine Menge Z, welche die Nullmenge als Element enthält und so beschaffen ist, daß jedem ihrer Elemente a ein weiteres Element der Form {a} entspricht ... Die Menge Z_0 enthält die Elemente 0, {0}, {{0}}, usw. und möge als "Zahlenreihe" bezeichnet werden, ...  Sie bildet das einfachste Beispiel einer "abzählbar unendlichen" Menge. [E. Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen (1908), S. 266]
 Regards, WM
 

And where does that use the term "Induction"
It translates to:
But in order to secure the existence of "infinite" quantities, we still need the following axiom, the essential content of which derives from Mr. Dedekind. ... The domain contains at least one set Z, which contains the zero set as an element and is such that each of its elements a corresponds to another element of the form {a} ... The set Z_0 contains the elements 0, {0}, {{0}}, etc., and may be called a "series of numbers", ... It is the simplest example of a "countably infinite" set. [E. Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen (1908), p. 266]
No "Induction"
I guess you are just showing you don't know what you are talking about.
The best I can tell is you are trying to claim that the German Language is incapable of actually properly using a word for Induction, even though the papers you are talking about probably do use the German translation of that word elsewhere, but you are too stupid to figure out the difference.