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

On 10/31/2024 1:24 AM, WM wrote:

On 30.10.2024 21:24, FromTheRafters wrote:

WM explained :

On 30.10.2024 16:43, FromTheRafters wrote:

on 10/30/2024, WM supposed :

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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.

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Wrong.

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What? ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ?

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No, the other part. Your 'conclusion' is a non sequitur.

 My conclusion is that all unit fractions are separated by large sets of real points from each other. Never two or more unit fractions are at the same point. Is that what you doubt? Hardly.

Huh?
1/1, 1/2, 1/3, ...
They are all by themselves and unique. Why are you trying to bring reals into a talk about unit fractions? All unit fractions are real, not all reals are unit fractions... Got it?
Go back to school.

 Then you must doubt that NUF(x) can grow only by 1 at any point x? But why?
 Regards, WM