Re: Replacement of Cardinality

On 8/19/24 7:32 AM, WM wrote:

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.
 Regards, WM
  

>
But, you can't just claim sommething is there that isn't.
>
The Number system is DERIVED from rules. Those rules DEFINE which numbers are, (and thus what are not).
>
You can not derive a first number > 0 in any of the Number System that we have been talking about, Unit Fractions, Rationals or Reals, so you can't claim it to exist.