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

On 29.10.2024 12:09, Richard Damon wrote:

On 10/29/24 4:42 AM, WM wrote:

NUF(x) MUST jump from 0 to Aleph_0 at all real values x, as below ANY real number x, there are Aleph_0 unit fractions.

That is wrong. It holds only for the reals which you know: The definable reals.

 

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No, but the first steps happen at undefinable x.

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

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Then it is dark.

 And, as you said above, NOT REAL.

A real number but not a definable real number.

 

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If you allow your NUF to accept infintesimal numbers

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No, that is strongly forbidden.

 Then it just jumps.

Believe what you like without foundation.
If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of not more than 1.
Regards, WM