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

WM was thinking very hard :

On 27.10.2024 20:01, FromTheRafters wrote:

WM pretended :

Am 27.10.2024 um 14:39 schrieb FromTheRafters:
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If 'not defined' could be a proper subset of the naturals, then there would be a first such 'not defined' in that subset. Of course WM can't substantiate any of his wild claims.

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Proof:

 Blah blah blah.

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Very substantial.
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Proof: If infinity is actual,

There need not be any distinction between infinity and your always finite but increasing sequence of sets. Infinite means not finite.

then all elements of the set of unit fractions exist.

They do anyway.

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

Followed by a discontinuity.

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

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

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

Non sequitur. This is just the second part of your stepwise function. It doesn't have to happen step by step as you envision it.

Of course x' and x'' are

Blah blah blah.