Re: Replacement of Cardinality

On 2024-08-19 11:32:44 +0000, WM said:

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?

 

But there is no point (>0) where it has a finite value,

 You can't see it and you are unable to derive it from mathematics. But blindness is not an argument.

Blindness is indeed much weeker than a proof but you may use it
as an argument as long as you can't find anything better.
--
Mikko