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

On 31.10.2024 09:29, FromTheRafters wrote:

WM submitted this idea :

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.

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

 Because NUF() doesn't "grow" it just *is*.

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According to set theory every function just "is". But we analyze or describe its behaviour with increasing argument x as increasing, constant or decreasing. Should that be forbidden in case of NUF in order to avoid problems?