Re: The set of necessary FISONs

On 23.02.2025 14:55, Jim Burns wrote:

On 2/23/2025 5:34 AM, WM wrote:

On 22.02.2025 21:29, Jim Burns wrote:

On 2/22/2025 5:17 AM, WM wrote:

 

We can remove all numbers from Z_0
and produce the empty set.

>
We can remove all numbers from {137}
and produce the empty set.
>
{137} ≠ 137

>
If we remove all numbers from {137}
we produce { },
if we remove all numbers from 137
nothing remains.
It is a matter of taste
whether the empty set is nothing.

 Nothing is what is in {}.
{{}} ≠ {}
Nothing is not what is in {{}}.
 The set of all FISONs with
each omissible FISON omitted
is {F}\{F} = {}

Right. UF = ℕ ==> Ø = ℕ.

 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. We omit all F(n) which amounts to remove F. Like all natural numbers amount to ℕ (not {ℕ})

Homework: Show the same for the set of FISONs.

 {{}} ≠  {}
 

Wrong.
Regards, WM