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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 25 Feb 2025 10:45:02 +0100
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On 24.02.2025 19:09, joes wrote:
> 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:

>>>>> {{}} ≠ {}
>> It is wrong to apply this in the present framework.
> Yes, you are wrong trying to talk about N \ {N}.

I never did.
> 
>>>> 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.

No that is from Burns.

> Properties don’t transfer from elements to their set.

The property of not existing transfers from all elements to the 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.

Proofs about the absence of all natural numbers prove the absence of ℕ.

Regards, WM