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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 30 Sep 2024 17:12:35 +0200
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On 29.09.2024 21:56, Jim Burns wrote:
> On 9/27/2024 2:54 PM, WM wrote:

> What you want is
> to tell us we've been wrong about sets.

You have been wrong about sets. You assume that sets are invariable but 
you don't assume that all elements, here unit fractions, can be detected.
>>> For each positive point x
>>> for each number (cardinality) k which can increase by 1
>>> there are more.than.k unit.fractions between 0 and x
>>
>> That is a misinterpretation of
>> the law valid for small numbers.
> 
> | "If the law supposes that," said Mr. Bumble,
> | squeezing his hat emphatically in both hands,
> | "the law is a ass — a idiot."
> |
> -- Charles Dickens, "Oliver Twist"

Not yet an ass, an idiot? Shakespeare English?
>> For every x NUF increases by not more than 1.
> 
> For every x>0 and x′>0
> NUF increases by not more and not less than 0.

Wrong.

> 🎜 Aleph.naught bottles of beer on the wall,

ℵo unit fractions cannot come into being without a first one.

Regards, WM