Re: How many different unit fractions are lessorequal than all unit fractions?

On 9/5/24 10:29 AM, WM wrote:

On 05.09.2024 16:22, Moebius wrote:

Am 05.09.2024 um 09:30 schrieb Chris M. Thomasson:

On 9/4/2024 5:38 PM, Richard Damon wrote:

>
>
 >>> one [unit fraction] sit[s] closest to zero. [WM]
>

nope, NONE [no unit fraction] sit[s] closest to zero, as there are always more that are closer.

>
Right.

 Wrong.
 NUF(x) increases from 0 to ℵo. But it cannot increase to ℵo at one point x > 0 because at every point there is at most one unit fraction.  Before ℵo there come 1, 2, 3, ...
 Regards, WM
 

Since it needs to find ℵo such points BEFORE we get to any of the finite values, you need to admit that either NUF(x) isn't defined or you have some other post-finite number system in view, which you logic is just incapable of handling since it can't even handle the infinite set of Natural Numbers.