Path: ...!feeds.phibee-telecom.net!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: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Wed, 2 Oct 2024 15:49:25 +0200
Message-ID: <vdjj14$11njf$1@solani.org>
References: <vb4rde$22fb4$2@solani.org>
 <298dcb6f-5f58-48b6-80e3-34260bf721f8@att.net> <vcn8n8$1nfqa$1@dont-email.me>
 <283c426f-ab1c-4ef0-a06c-1bf7d28a2cfa@att.net> <vcpo5e$29qe5$1@dont-email.me>
 <6b50a171-8127-4ce6-9bd3-2dc213638e9b@att.net> <vcroj3$2nfvb$2@dont-email.me>
 <519db81b-4a4d-417d-8cd2-7fef5a342efd@att.net>
 <6704347e-2f99-40f2-887f-de93f6fdd659@tha.de>
 <d10dbfab-9235-4fcd-a892-b407029e8f1d@att.net>
 <8b3e744d-3419-40c3-a7c6-fe59edd528a9@tha.de>
 <851e9929-8ab7-49d1-b478-e65c61fba2e3@att.net> <vd1bis$3njbp$7@dont-email.me>
 <d0da206d-e1c9-4a32-8ec7-64e1365a8f3e@att.net> <vd6v0d$qj9u$2@dont-email.me>
 <78a0f795-f1c0-4ba5-90f9-acf667968011@att.net> <vdef52$29746$3@dont-email.me>
 <aec625a9-581f-4692-b20f-831b9f121e52@att.net> <vdes49$2bj6r$2@dont-email.me>
 <adea0828-b2b1-4273-8e99-8c143f17f4f1@att.net> <vdhbhg$2qovr$1@dont-email.me>
 <fd9f0e31-89f5-46db-b1d9-f6f818901b2c@att.net> <vdj9mg$3713m$1@dont-email.me>
 <dd3ae20b43fcca9509267b031878c89b6b5c229f@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 2 Oct 2024 13:49:24 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="1105519"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:fzpRptliZJw3M+P/nIzzwoYWghs=
X-User-ID: eJwFwYkBwEAEBMCWcCwpx9t/CZmxB0a7wqB2doEojhTgVGgpBit45M2aGwWpFBPokr9Unvtq6LqmC7f7Azn0Fec=
Content-Language: en-US
In-Reply-To: <dd3ae20b43fcca9509267b031878c89b6b5c229f@i2pn2.org>
Bytes: 2768
Lines: 18

On 02.10.2024 14:56, joes wrote:
> Am Wed, 02 Oct 2024 13:10:09 +0200 schrieb WM:
>> On 01.10.2024 22:05, Jim Burns wrote:
>>> On 10/1/2024 1:29 PM, WM wrote:
>>
>>> This is incorrect:
>>> 🛇⎛ ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  shows that 🛇⎜ at no point x 🛇⎝ NUF can
>>> increase by more than one step 1.
>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  doesn't show that.
>> You believe that more than one unit fractions can occupy one and the
>> same point nevertheless? That would make the distance 0, but it is > 0.
>> Therefore you are wrong.
> Nobody believes that. It just doesn’t follow.

It follows that either all unit fractions are at different places (then 
NUF grows one by one) or not. Then at least two are at the same place. 
There are no further alternatives.

Regards, WM