Re: The set of necessary FISONs

Am Sun, 23 Feb 2025 17:26:27 +0000 schrieb joes:

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.

Induction produces ℕ, not only a finite number.

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.

Therefore your posts are irrelevant and will no longer be read.