Re: The set of necessary FISONs

Am Thu, 27 Feb 2025 20:50:11 +0100 schrieb WM:

On 27.02.2025 19:19, Jim Burns wrote:

On 2/27/2025 5:45 AM, WM wrote:

On 26.02.2025 23:17, Jim Burns wrote:

By the same induction I prove UF = ℕ  ==> Ø = ℕ.

What you use to prove that is ∀n:Aᴺ(n) ⇒ A(ℕ)

That is how Zermelo guarantees Z₀.

Absolutely not. He does not prove Z e Z.

That's not induction.
It seems to follow from confusion over the difference between a set and
its elements.

There is no difference in some cases like these:
When all n are added by induction to the empty set, then we have
constructed ℕ.
When all n are subtrated  by induction from ℕ then we have created the
empty set.

There totally is a difference between N and each of its elements.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.