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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 25 Feb 2025 10:37:19 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Tue, 25 Feb 2025 10:55:35 +0100 schrieb WM:
> On 25.02.2025 10:17, joes wrote:
>> Am Tue, 25 Feb 2025 10:02:47 +0100 schrieb WM:
>>> On 24.02.2025 19:01, joes wrote:
>>>> Am Mon, 24 Feb 2025 15:59:18 +0100 schrieb WM:
>>>
>>>>> These axioms can be applied to show that all FISONs can be removed.
>>>> Nope. Any number of them can be removed. Indeed, removing all changes
>>>> the union, as you have admitted.
>>> There are not more than any number.
>> There are more FISONs than any natural number: infinitely many.
> Yes potential infinity. There are more FISONs than any fixed natural
> number, but the number of FISONs is a natural number
Immediate contradiction: there is no largest natural.

> because the sequence
> {1}
> {2, 1}
> {3, 2, 1}
> ...
> has no limit.
It does, actually, converge on N.

> Further induction produces no actual infinity.
WDYM "further"? Induction goes up to infinity.

>>>>> Only all FISONs = natural numbers are the matter of my proof.
>>>>> According to Zermelo they make up the set ℕ.
>>>> The set N is not a natural number
>>> Of course. Nobody said so.
>> You pretend to remove the whole set.
> I remove by induction all natural numbers. What of ℕ remains in your
> opinion?
Huh? 

>>> But Zermelo claims to produce the set ℕ. Is he wrong?
>>> Hint: In fact he produces ℕ_def.
>> No, you are wrong.
> You claimed yourself that induction produces only a finite number of
> elements. Zermelo used induction.
I didn't. The *elements* are finite.

-- 
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.