Re: Replacement of Cardinality

On 8/15/24 9:57 AM, WM wrote:

Le 14/08/2024 à 21:01, "Chris M. Thomasson" a écrit :

On 8/14/2024 5:28 AM, WM wrote:

 

The existence of a smallest unit fraction is the only alternative to the existence of more than one at a real point.

>
There is no smallest unit fraction,

 There is a smallest one because all are separated:
 ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
Regards, WM

Actually, that statement says that there is no smallest, as for every 1/n there exist a smaller 1/(n+1).
If n+1 didn't exist, then your statement wouldn't be true for all n.