Re: Replacement of Cardinality

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