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

Am Sun, 27 Oct 2024 17:12:23 +0100 schrieb WM:

Am 27.10.2024 um 14:54 schrieb Moebius:

Am 27.10.2024 um 08:38 schrieb WM:
 

and after NUF(x') = 1

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

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.

That is blatantly wrong because it would require that ℵo unit fractions
exist between 0 and each and every x > 0,

Which is obviously the case. If there were a real x with finitely many
UFs less than it, the finitely many larger UFs... couldn't have
infinitely many lesser UFs. Unless you claim finitely many UFs.

i.e., the open interval (0, 1].

No, you shifted the quantifiers again.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.