Re: Replacement of Cardinality

On 8/17/24 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?
 Regards, WM

But there is no point (>0) where it has a finite value, so it just isn't a defined function for x>0.
Sorry, you just don't understand how math works, because it seems you only know counting on your fingers.
The can NOT be a greatest Natural Number because of how they are defined.
If you natnumber are something different, then you need to try to define them and work out their properties,
Then tell people what they can do with your fake "natnumbers" that is better than the real Natural Numbers.