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

On 29.10.2024 00:58, Richard Damon wrote:

On 10/28/24 3:42 PM, WM wrote:

I mean that there are unit fractions.
None is below zero.
Mathematics proves that never more than one is at any point.
>

Which doesn't mean there must be a first, as they aproach an accumulation point where the density becomes infinite.

Their density is bounded by uncountably many points between every pair of consecutive unit fractions:
∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
The density is one point over uncountably many points, that is rather precisely 0.

 Something which can't happen your world of finite logic, but does when the logic can handle infinities.

Where does the density surpass 1/10? Can you find this point? If not it is another proof of dark numbers.
Regards, WM