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

On 10/3/24 2:34 PM, WM wrote:

On 03.10.2024 01:03, Richard Damon wrote:

On 10/2/24 7:57 AM, WM wrote:

 

Of course all gaps between unit fractions are made of more than finitely many points. I never denied that.

>
But that also means that no point are "next to" each other.

 Therefore NUF can increase at most by 1 at every real point.

Why?
If NUF(x) counts the unit fractions u < x, then NUF doesn't increase at ANY points, as the "point" it increases isn't a point, but the adjacently that isn't a point to the unit fractions,
If NUF(x) counts the unit fractions u <= x, then there isn't a point for NUF(x) to increase by 1 and there isn't a "smallest" unit fraction to increase from 0 to 1, as EVERY unit fraction has smaller unit fractions than itself (Aleph_0 of them to be exact), and also it doesn't increase by one at any of the finite unit factions, as it has already reached Aleph_0 by them, and Aleph_0 can't be "increased" by 1, as that is still the same number.

 

>
Try to learn the basics and to understand ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

>
Which means that for all n that are in the Natural numbers, for the unit fraction  1/n, theree DOES EXIST another unit fraction 1/(n+1) that is smaller than it.

 That is true for all visible and most dark numbers bu not for all.

But all Natural Nunbers are visible, as they havd a definition, and thuys you are just admitting that your logic system doesn't actually have the Natural Nubmers, because you logic has just been exploded by its inconsistanc, and you are shos to be nothing by an ignorant liar.
All you are doing is showing you don't know what the Natural Numbers are defined to be, and then LIE about their properties.

 Regards, WM