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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 27 Oct 2024 18:04:38 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.

-- 
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.