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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Sun, 16 Mar 2025 13:09:17 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 15 Mar 2025 18:13:57 +0100 schrieb WM:
> On 15.03.2025 12:57, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
> 
>> I'm showing you that your "definition" of "definable numbers" is no
>> definition at all.
> You are mistaken. Not all numbers have FISONs because ∀n ∈ U(F): |ℕ \
> {1, 2, 3, ..., n}| = ℵo.
> ℵo nubers have no FISONs.
Those are, by definition, not naturals.

>>>>> Obviously the subtraction of all numbers which cannot empty ℕ cannot
>>>>> empty ℕ. Therefore |ℕ \ ℕ_def| = ℵo. Do you agree? 
>>>> Of course not.
>>> Then you cannot think logically.
>> When confronted with your misguided attempts at mathematics, it is very
>> difficult to follow your "logic", much less agree with it.
> The subtraction of all numbers which cannot empty ℕ cannot empty ℕ.
> Simpler logic is hardly possible.
This is so fucked up. If you take out everything, nothing remains.

>>>> It all depends on the X from which N_def is formed.  If X is N \ {1},
>>> Then its elements are mostly undefined as individuals.
>> "Undefined as individuals" is an undefined notion,
> No. It says simply that no FISON ending with n can be defined.
Then n is infinite and not in fact natural.

>>> Every element has a finite FISON. ℕ is infinite.  Therefore it cannot
>>> be emptied by the elements of ℕ_def and also not by ℕ_def.
>> A "finite" FISON?  What other type is there?  What do you mean by
>> "having" a FISON?  What does it mean to "empty" N by a set or elements
>> of a set?  What is the significance, if any, of being able to "empty" a
>> set?
> Simply try to understand. I have often stated the difference:
> ∀n ∈ U(F): |ℕ \ {1, 2, 3, ..., n}| = ℵo ℕ \ {1, 2, 3, ...} = { }
It does not say what you think it says.

>> None of these notions are standard mathematical ones.  If you want to
>> communicate clearly with mathematicians, you'd do far better if you
>> used the standard words with their standard meanings.  But maybe you
>> don't want to communicate clearly.
>> 
>>>>>> The tending takes place, but not in a "place". 
>>>>> No? Tending means that hitherto undefined natural numbers become
>>>>> defined. That takes place on the ordinal line.
>>>> "Hitherto" ("bis jetzt" in German) is purely a time based adverb. 
>>>> The natural numbers are not defined in a time based sequence.  They
>>>> are defined all together.
> The set is defined, not its elements. All defined elements
You can't have a set with undefined elements.

>>> Not the defined numbers.
>> "Defined numbers" remains (still) undefined.
> Defined numbers have FISONs ad cannot empty ℕ.
Yes they can. There are no other numbers.

> They are placed on the
> ordinal line and can tend to ℕ. This cn happen only on the ordinal line.
> Your assertion of the contrary is therefore wrong.
> 
>> "Defined numbers" appears not to be a coherent mathematical concept.
> The subtraction of all numbers which cannot empty ℕ cannot empty ℕ. The
> collection of these numbers is ℕ_def.

-- 
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.