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? (infinitary)
Date: Thu, 31 Oct 2024 07:36:41 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <db195c8b7f05657f444b36a449fda7b12489447d@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <vf8r7k$1jnia$2@dont-email.me>
 <d316baa3-de5b-4644-86ff-beacad9df107@att.net> <vfd97u$2jtos$1@dont-email.me>
 <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <vfe5d5$2olom$1@dont-email.me>
 <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <vfg07k$1chpe$1@solani.org>
 <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <vfgil3$38pn6$1@dont-email.me>
 <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me>
 <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org>
 <vfjg9h$3rjvp$2@dont-email.me> <vfkqlr$3fii$1@solani.org>
 <vfl8o7$3mnmt$4@i2pn2.org> <vflfq9$f82l$1@dont-email.me>
 <vflovl$1fpr2$3@solani.org> <vfm2m5$iasq$1@dont-email.me>
 <vfnmo3$ui6v$1@dont-email.me> <vfo5rf$1178s$1@dont-email.me>
 <vfoqqr$14lcc$2@dont-email.me> <vfotg8$15r9a$1@dont-email.me>
 <0e5fb47d-60f7-42bb-beec-4a9661c807da@tha.de> <vfqbrm$1gqu7$1@dont-email.me>
 <vft6n5$246cp$5@dont-email.me> <vftago$25nkf$1@dont-email.me>
 <vftedi$26a4v$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 31 Oct 2024 11:36:41 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="286438"; 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: <vftedi$26a4v$1@dont-email.me>
Bytes: 2714
Lines: 21

On 10/30/24 10:04 AM, WM wrote:
> On 30.10.2024 13:57, FromTheRafters wrote:
>> WM explained :
> 
>>> NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by 
>>> more than 1 at any point x of the real axis.
>>
>> The number of unit fractions less than x is always aleph_zero for 
>> positive x.
> 
> Believe what you like without foundation.
> If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of not 
> more than 1.
> 
> Regards, WM
> 

No, what that expression shows is that for every n, the unit fraction 
1/n has another unit fraction 1/(n+1) that is smaller than it, so there 
is no "first" unit fraction in that sense for NUF(x) to get to 1.

You are just proving you don't undetstand even your own mathematics.