Sujet : Re: The set of necessary FISONs
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 24. Feb 2025, 18:10:26
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vpi962$18qai$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
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>>
>
{{}} ≠ {}
>
Wrong.
It is wrong to apply this in the present framework.
Zermelo creates all natural numbers by induction and by that guarantees the existence of the set ℕ.
These axioms can be applied to show that
all FISONs can be removed.
{1,2}\{1,{2}} = {2}
Only such nonsense available?
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.
Claims about each natural number
are silent about ℕ.
Claims about the existence of all natural numbers are claims about the exitstence of ℕ.
Um aber die Existenz "unendlicher" Mengen zu sichern, bedürfen wir noch des folgenden ... Axioms. [Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266]
The elements are defined by induction in order to guarantee the infinite set.
Regards, WM
The set of necessary FISONs
Re: The set of necessary FISONs