Re: Replacement of Cardinality

Le 17/08/2024 à 16:29, Richard Damon a écrit :

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.

There is a Mückenheimish way to "prove" that you do not need fingers
to count up to 4 on your fingers.
Check the index finger : not necessary. One can count using the other
ones.
Check the middle finger : not necessary. One can count using the other
ones.
Check the ring finger : not necessary. One can count using the other
ones.
Check the little finger : not necessary. One can count using the other
ones.
Check the thumb : not necessary. One can count using the other  ones.
Therefore *all* fingers are unnecessary: one can count up to four even
if he has no fingers at all.