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

On 9/23/24 8:57 AM, WM wrote:

On 22.09.2024 22:22, Jim Burns wrote:
 > On 9/22/2024 2:37 PM, WM wrote:
 >> On 22.09.2024 19:44, Jim Burns wrote:
 >
 >>> There is no point next to 0.
 >
 >> There is a smallest unit fraction
 >> because
 >> there are no unit fractions without a first one
 >> when counting from zero.
 >
 > Each visibleᵂᴹ unit.fraction ⅟k has
 > a counter.example ¼⋅⅟k to its being smallest.
 Yes. Therefore the smallest unit fraction must be dark.

Which is something that doesn't exist.
Your "Darkness" is just a method you are trying to use to hide the fact that your logic is just broken.
NO actual Unit Fraction is "dark" as ALL of them are usable individually (it would just take infinite work to actually use all of them).
Thus, your "Dark" numbers aren't actually Unit Fractions, but something else that you want to CALL unit fractions to make you logic seem to work, but just actually blow it up more.

  > No positive point, unit.fraction or otherwise,
 > is NOT undercut by some visible unit fraction.
 Wrong. NUF(x) grows from 0 to more. This increase cannot avoid 1 because of ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
 Regards, WM

Which is why NUF(x) isn't actually possible to exist by your definition, There is *NO* finite number x where NUF(x) can be 1, and thus it is just a mis-defined function.
Sorry, you are hanging your logic on contradictions, which has made your brain, and the logic system, just explode in the errors it makes from contradictions.