Re: The set of necessary FISONs

Am Mon, 24 Feb 2025 18:10:26 +0100 schrieb WM:

On 24.02.2025 17:36, Jim Burns wrote:

On 2/24/2025 9:59 AM, WM wrote:

On 23.02.2025 23:03, Jim Burns wrote:

On 2/23/2025 2:32 PM, WM wrote:

On 23.02.2025 19:34, Jim Burns wrote:

On 2/23/2025 9:43 AM, WM wrote:

 

There is no reason to consider {{F}} at all.

There is reason, but only for people wantcing to be correct.

Peano, Zermelo, or v. Neumann

...agree that {{F}} ≠ {F}

and also that 3 ≠ pi.

<WM<JB>>

>
{{}} ≠ {}

It is wrong to apply this in the present framework.

Yes, you are wrong trying to talk about N \ {N}.

These axioms can be applied to show that all FISONs can be removed.

{1,2}\{1,{2}} = {2}

Only such nonsense available?

That is your nonsense. Try and formalise your shit.

The set of finite ordinals after v. Neuman is undoubtedly such a set.

The set of finite ordinals after v. Neumann is not a finite set.
A claim for each of its elements is silent about the set.

You are wrong. The existence of the set is guaranteed by elements which
are defined by induction. Note that induction has been invented for
proofs concerning infinitely many element.

That has no bearing. Properties don’t transfer from elements to their set.

Claims about each natural number are silent about ℕ.

Claims about the existence of all natural numbers are claims about the
exitstence of ℕ.

We are not disputing the existence.

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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.