Re: The set of necessary FISONs

Am Sun, 23 Feb 2025 18:08:25 +0100 schrieb WM:

On 23.02.2025 16:37, joes wrote:

Am Sun, 23 Feb 2025 15:43:48 +0100 schrieb WM:

 

Right. UF = ℕ ==> Ø = ℕ.

No. As we've seen, you cannot omit all FISONs.

Which one cannot?

All. All FISONs can not be omitted, only a finite number,
though it doesn't matter which. If you omit all, you get
a different set than when omitting any one.

The set of all FISONs with the set of omissible FISONs omitted is
{F}\{{F}} = {F}

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

Indeed, because {F} is not an element of F, which is why I'm wondering
why you keep talking about it.

And cutting this.

We omit all F(n) which amounts to remove F.

No, it amounts to the elements of F, not those of {F}.

All elements F(n) of F are F.

No, the set F is not {F}. F is the set *of its elements*. F is not an
element;

Like all natural numbers amount to ℕ (not {ℕ})

Like all FISONs amount to F, not {F}.

So it is.

Thus F \ {F} = F. It doesn't even make sense to remove F from F.

--
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.