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Subject: Re: Replacement of Cardinality
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 17/08/2024 à 23:39, Jim Burns a écrit :
> On 8/17/2024 9:28 AM, WM wrote:
>> Le 16/08/2024 à 19:39, Jim Burns a écrit :
> 
>>> no element of ℕᵈᵉᶠ is its upper.end,
>>> because
>>> for each diminishable k
>>> diminishable k+1 disproves by counter.example
>>> that k is the upper.end of ℕᵈᵉᶠ
>>
>> SBZ(x) starts with 0 at 0 and increases,
>> but at no point x it increases by more than 1
>> because of
>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
>> Therefore there is a smallest unit fractions 
>> and vice versa a greatest natnumber.
>> What can't you understand?
> 
> How can ½⋅β
> ⎛ half the allegedly.positive greatest.lower.bound β of
> ⎝ visibleᵂᴹ.unit.fractions

Visible unit fractions have the lower bound 0.
Dark unit fractions have a smallest element. No smaller unit fractions is 
existing because no larger natnumber is existing.

Regards, WM