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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 23 Feb 2025 15:43:48 +0100
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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