Re: The set of necessary FISONs

On 2/22/25 5:22 AM, WM wrote:

On 22.02.2025 02:05, Richard Damon wrote:
 

Since that is the earlier work, and not the later refined work, maybe you should update your studies. (Note this creates Z, not N)

 Zermelo's Z_0, the set of numbers is a subset of Z.

Which still isn't N, and thus can't be useded as N.

>
Note, as I understand it, that initial Zermelo Set Theory didn't even HAVE "induction",

 You don't understand it.

Sure I do, you are the one using the wrong words.

 

but its last axiom was the Axiom of Infinity that say that there exists in this domain the set Z that contains the null set as an element and is so constituted that to each of its element a, there corresponds a further element of the form {a}, in other words with each of its elements a, it also contains the corresponding set {a} as an element.

 That is induction.

Nope, maybe you don't understand what INDUCTION actually is.

>
Note, this is NOT the statement of induction.

 You are wrong. Remember Peano's successors.

Peano's successors are not induction.
Induction is the axiom that lets your prove that a set contains the set of Natural Numbers. It isn't a "construction" technique.
Maybe the prohlem is that the German you know doesnt understand what the word means, and you are confusing to seperate but related ideas.

 Regards, WM