Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Thu, 3 Oct 2024 21:23:22 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <0eae4f35990041c80ca2c21fddc3261a2e0e7577@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <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> <vdj9rn$3713m$2@dont-email.me>
 <67e26dda-ec44-4927-82ac-dfc17dc3d07d@att.net> <vdmni6$3r0us$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 4 Oct 2024 01:23:22 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="466071"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
In-Reply-To: <vdmni6$3r0us$1@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
Bytes: 2889
Lines: 30

On 10/3/24 2:25 PM, WM wrote:
> On 02.10.2024 22:07, Jim Burns wrote:
>> On 10/2/2024 7:12 AM, WM wrote:
>>> On 01.10.2024 22:05, Jim Burns wrote:
>>
>>>> For every nonzero distance d from 0
>>>> there are ℵ₀.many unit.fractions closer than d
>>>
>>> That means
>>> there is no d by what
>>> you can distinguish ℵ₀ unit fractions?
>>
>> You (WM) require us to guess
>> what you mean by 'distinguish'.
> 
> You distinguish two unit fractions 1/n and 1/m if you place a point in 
> distance d from 0 between them: 1/n < d < 1/m.
>>
>> There is no d between
>> ℵ₀.many.smaller.unit.fractions and
>> slightly.fewer.than.ℵ₀.many.smaller.unit.fractions.
> 
> That means you cannot distinguish ℵ₀ smaller unit fractions.
> 
> Regards, WM

Sure we can, we just can't find any that have less than Aleph_0 numbers 
below them since those numbers don't exist.

Your logic just can't handle numbers like Aleph_0, and thus has exploded 
your brain when you made it try.