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

On 27.10.2024 19:00, Richard Damon wrote:

On 10/27/24 12:12 PM, WM wrote:

Am 27.10.2024 um 14:54 schrieb Moebius:

Am 27.10.2024 um 08:38 schrieb WM:
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and after NUF(x') = 1

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There is no x' e IR such that NUF(x') = 1.

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If all unit fractions are existing, then there is each one. Never two or more are at the same point. Hence there is a single one first.

 No two together, but no need for one to be first at the large 'n' end of them.

NUF increases by 1 or more, but more would violate mathematics.

Hint: For each and every x e IR, x <= 0: NUF(x) = 0
and for each and every x e IR, x > 0: NUF(x) = aleph_0.

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That is blatantly wrong because it would require that ℵo unit fractions exist between 0 and each and every x > 0, i.e., the open interval (0, 1].

Right, like is what happens.
 It may seem strange to a person stuck in finite logic, but is true when you understand how infinity works.

This infinity between 0 and (0, 1] is not what I can accept.
Regards, WM