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Subject: Re: Replacement of Cardinality
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 31/07/2024 à 19:33, Jim Burns a écrit :
> On 7/31/2024 9:59 AM, WM wrote:
>> Le 30/07/2024 à 20:37, Jim Burns a écrit :
> 
>>> NUF(x) = |⅟ℕ∩(0,x]| = ℵ₀
>>> does not imply any unit fraction outside (0,x]
>>
>> But it implies that you can use only
>> x having ℵ₀ smaller positive points,
>> in fact even ℵ₀*2ℵ₀.
>>
>> ∀ x > 0: NUF(x) = ℵ₀ would be wrong.
> 
> Each non.{}.subset of ⅟ℕ∩(0,1] is maximummed.
>   ∀S ⊆ ⅟ℕ∩(0,1]: S ≠ {}  ⇒  ∃u = max.S

In the dark domain the maximum cannot be discerned.
> 
> Each unit.fraction in ⅟ℕ∩(0,1] is down.stepped.
>   ∀u ∈ ⅟ℕ∩(0,1] ∃v = ⅟(1+⅟u) = max.⅟ℕ∩(0,u)

Assuming all this would lead to potential infinity.
I assume actual infinity however. There are dark numbers. There is a 
greates natnumber. There is no chance to lose Bob.

Regards, WM