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

On 9/13/24 1:16 PM, WM wrote:

On 12.09.2024 23:40, Moebius wrote:

Am 12.09.2024 um 22:36 schrieb Chris M. Thomasson:

On 9/2/2024 10:07 AM, WM wrote:

>

How many different unit fractions are lessorequal than all unit fractions?
>
[The correct] answer is that one unit fraction is lessorequal than all unit fractions. [...]

>

[In math] there is only the one correct answer given above.

>
Indeed,

 Mathematical proof: NUF grows from 0 to more. At no point it can grow by more than 1.
 Regards, WM
 

And at no point can it grow by ONE, so it doesn't actually exist.
For every finite x, there are Aleph_0 unit fractions below it, and Aleph_0 doesn't "grow" when you try to add 1 to it.
Also, there is no finite point where NUF(x) can grow from 0 to 1, as any such x, as more than 1 unit fraction below it.
Thus, what we can prove is that NUF(x) can not actually be defined as a finite function of finite values.
Sorry, you are just proving that you brain exploded into smithereens from the inconsistencies of your logic when you try to deal with systems with infinities in them.