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

On 29.10.2024 01:21, Richard Damon wrote:

On 10/28/24 3:52 PM, WM wrote:

On 28.10.2024 12:21, Richard Damon wrote:

On 10/28/24 6:36 AM, WM wrote:

>

NUF increases by 1 or more, but more would violate mathematics.

>
No, NUF(x) jumps from 0 to Aleph_0 in the domain of finite numbers, because there is no finite x where it has the value of 0.

>
It has the value 0 for all x =< 0. And it cannot jump by more than 1 at any point.

 Of course it can. just not at any finite value.

There are no others on the real line.

No, but the first steps happen at undefinable x.

 No, it happens at an x that isn't a finite number.

The it is dark.

 If you allow your NUF to accept infintesimal numbers

No, that is strongly forbidden.

This infinity between 0 and (0, 1] is not what I can accept.

>
Note, it isn't an "infinity between" it is that the "bottom" of (0, 1] doesn't exist as a definable point.

>
That is true. The bottom is dark.

 No, the bottom is outside the set.

Then it is dark bottom.

 Your "Darkness" is just your attempt to hide the problems with your logic.

And your bottom outside the set is what?
Regards, WM