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

On 28.10.2024 21:51, FromTheRafters wrote:

WM explained :

On 28.10.2024 15:07, FromTheRafters wrote:

WM was thinking very hard :

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The function NUF(x) = Number of Unit Fractions between 0 and x starts with 0 at 0.

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Followed by a discontinuity.

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No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 holds everywhere.

 Not for n equal to zero.

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I said ∀n ∈ ℕ. 0 is no natural number. NUF(0) = 0.

After NUF(x') = 1 it cannot change to NUF(x'') =  2 without pausing for an interval consisting of uncountably many real points.

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Your "Axiom of because I say so" is overworked.

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It is mathematics:>> The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

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Non sequitur. This is just the second part of your stepwise function.

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It holds everywhere if mathematics holds everywhere.
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It doesn't have to happen step by step as you envision it.

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As mathematics dictates it.
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You have confessed: In order to maintain actual infinity without dark numbers, you have to violate mathematics.

 Bull! Just another of your non sequiturs.

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Try to argue mathematically in spite of spitting nonsense or be quiet.