Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 2 Sep 2024 19:07:58 +0200
Message-ID: <vb4rde$22fb4$2@solani.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Mon, 2 Sep 2024 17:07:58 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="2178404"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:i5whJ1dOqOYfOKAAmhnuEfambuA=
X-User-ID: eJwFwYEBACAEBMCVVP4xTsT+I3SHw8UyJagYTOsKi3XoqhXCexFZ80rO9ZnkPEuDhAyqPYttiY3cTe/EB1TwFgs=
Content-Language: en-US
Bytes: 1480
Lines: 15

How many different unit fractions are lessorequal than all unit 
fractions? The correct answer is: one unit fraction. If you claim more 
than one (two or three or infintely many), then these more must be 
equal. But different unit fractions are different and not equal to each 
other.

Another answer is that no unit fraction is lessorequal than all unit 
fractions. That means the function NUF(x)
Number of UnitFractions between 0 and x > 0
with NUF(0) = 0 will never increase but stay at 0. There are no unit 
fractions existing at all.

Therefore there is only the one correct answer given above.

Regards, WM