Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!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: Tue, 10 Sep 2024 07:49:18 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <b2ef3be05e2cb212c9b458f146c7ebbcbec875ef@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <vb6o0r$3a4m1$2@dont-email.me>
 <7e1e3f62-1fba-4484-8e34-6ff8f1e54625@att.net> <vbabbm$24a94$1@solani.org>
 <06ee7920-eff2-4687-be98-67a89b301c93@att.net>
 <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp>
 <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> <vbd56i$fqa0$1@dont-email.me>
 <vbdbq3$gdoe$2@dont-email.me> <vbes57$qdqo$2@dont-email.me>
 <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org>
 <vbesjo$27gfe$1@solani.org> <vbf0s9$qp1j$3@dont-email.me>
 <vbfpf5$utdu$2@dont-email.me> <vbh5qe$19a45$1@dont-email.me>
 <vbhdf6$1btm1$1@dont-email.me> <vbhdsh$1btm1$2@dont-email.me>
 <vbhj65$1bi3k$3@dont-email.me>
 <9eeba8a5041ce7ee48e5019d9e98d4ea38a1eb72@i2pn2.org>
 <vbhkmo$1bi3l$8@dont-email.me>
 <89ed6d8de6c20d65e869d384181b642309f63bc4@i2pn2.org>
 <vbkv1r$20uoi$4@dont-email.me>
 <937a4a53c27b209538bb77bfe8059a90cc70ee9e@i2pn2.org>
 <vbl1fv$21n0s$4@dont-email.me> <vbmi8t$2ce0a$2@dont-email.me>
 <d4b86bde5086f0a2a4a5911ef002f3065b275f52@i2pn2.org>
 <vbn2bs$2em18$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 10 Sep 2024 11:49:18 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="1530636"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
In-Reply-To: <vbn2bs$2em18$2@dont-email.me>
Bytes: 3140
Lines: 31

On 9/9/24 10:57 AM, WM wrote:
> On 09.09.2024 13:46, joes wrote:
>> Am Mon, 09 Sep 2024 12:22:21 +0200 schrieb WM:
> 
>>> ℵo unit fractions cannot fit into one of the ℵo intervals between two of
>>> them, because ℵo unit fractions occupy ℵo intervals.
>> What? It’s about the size, not the number of intervals.
> 
> One of ℵo intervals is smaller than ℵo intervals.
> Unit fractions are real points on the real line. Therefore there is a 
> beginning, one or more smallest unit fractions.
> 
> Regards, WM
> 
> 
Where do you get that from?

Every interval is based on finite numbers, and only is smaller than a 
finite number of other intervals.

You have a funny-mental error that you think there must be a smallest.

Part of the problem is likely your concept of them being "real".

They are real in the sense that they exist by the definition of mathematics.

They are not real in the sense that they PHYSICALLY exist as a finite 
object in the universe. That would establish a lower limit to there 
size, whcih doesn't exist in the mathematical reality, and means they 
can't be actually infinite.

THis seems to be a source of your confusion.