Re: The set of necessary FISONs

On 2/20/25 12:57 PM, WM wrote:

On 20.02.2025 17:03, Jim Burns wrote:
 

>
Why do you think the set has the same property as
its elements?

 That is not true in general but can be proven in this case. See my other posting. Or see Frege: When all trees of a forest haven been burned, then the forest has been burned.

Nevertheless:
Zermelo proves
the existence of an inductive *set*
by induction.

>
You keep using that word.
I do not think it means what you think it means.

 Then read it and ponder over it until you recognize that he said it:
The elements are defined by induction in order to guarantee the infinite set. Um aber die Existenz "unendlicher" Mengen zu sichern, bedürfen wir noch des folgenden ... Axioms. [Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266]
 Regards, WM
 

But that isn't the translation I get for the statement:
In order to secure the existance of "infinite" sets, we still need the following axioms.
There is no mention of "induction" in the statement.
So, you are just showing that you don't understand what you are reading.