Re: Replacement of Cardinality

Le 02/08/2024 à 17:59, Richard Damon a écrit :

On 8/2/24 7:38 AM, WM wrote:

Le 01/08/2024 à 18:04, joes a écrit :

Am Thu, 01 Aug 2024 12:27:27 +0000 schrieb WM:

 

separated from 0 by any eps. Therefore your claim is wrong.

No. There is ALWAYS an epsilon.

 Failing to separate almost all unit fractions.
Don't claim the contrary. Define (separate by an eps from 0) all unit fractions. Fail.

>

Improperly revesing the conditionals.

Not at all! Recognizing that eps must be chosen. You cannot choose a eps that separates more than few unit fractions. That is why most cranks claim ∀x > 0:  NUF(x) ≥ ℵ₀. It holds or all x that can be chosen. How should there be always an epsilon smaller than every x > 0 which fails? ? ?
Regards, WM