Sujet : Re: The set of necessary FISONs
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 24. Feb 2025, 19:25:22
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <1bf6d76c-e7f0-4514-9271-d53945c095c0@att.net>
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 2/24/2025 12:10 PM, WM wrote:
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:
<WM<JB>>
>
{{}} ≠ {}
>
Wrong.
>
It is wrong to apply this
in the present framework.
In the present framework,
you (WM) confuse a claim about each FISON in {F}
with a claim about {F}
Zermelo creates all natural numbers by induction
and by that guarantees the existence of the set ℕ.
I guarantee that Zermelo was a finite being
and that, as such, he did not perform any supertask.
The existence of the set which
is its.own.only.inductive.subset
is proven from Zermelo's axioms.
We call that set ℕ.
If you (WM) call something else ℕ,
we are still discussing the set which
is its.own.only.inductive.subset.
These axioms can be applied to show that
all FISONs can be removed.
>
{1,2}\{1,{2}} = {2}
>
Only such nonsense available?
I'll grant you that it's trivial.
You (WM) have made it necessary to cover this.
{1,2}\{1,{2}} = {2}
Do you agree or disagree?
Claims about the existence of all natural numbers
are claims about the exitstence of ℕ.
In the domain of ST+F
( {}, X∪{y}, intensionality, finitude ),
each natural number exists,
but ℕ does not exist.