Re: The set of necessary FISONs

Am Fri, 28 Feb 2025 11:53:22 +0100 schrieb WM:

On 28.02.2025 11:34, joes wrote:

Am Fri, 28 Feb 2025 10:12:13 +0100 schrieb WM:

On 28.02.2025 01:00, Jim Burns wrote:

On 2/27/2025 5:01 PM, WM wrote:

>

Zermelo's approach does not extend ∀n:Aᴺ(n) to Aᴺ(ℕ)

It does. Zermelo says it, and it is easy to prove it:
Adding all natural numbers established the set ℕ.

Nonono. The set is not added to itself.

The set is established (not added) by all its elements.

Yes, but that is what you and Jim wrote above.

Wherever you got Lorenzen's approach from, send it back.

Then you admit to stand outside of mathematics. Lorenzen uses the same
induction as Cantor, Dedekind, Peano, Schmidt, Zermelo, or v. Neumann.
Addition of all natnumbers results in the set of all natnumbers.

No, the set of naturals is not a natural.

The set ℕ is constructed by adding all its numbers or FISONs:
ℕ = {1, 2, 3, ...}
=  {1} U {2} U {3} U ...
=  {1} U {1, 2} U {1, 2, 3} U ...

Yes, its elements, not itself.

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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.