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: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 31 Oct 2024 09:41:11 +0100
Message-ID: <vfvfr6$9264$5@solani.org>
References: <vb4rde$22fb4$2@solani.org> <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> <vftk73$277v9$1@dont-email.me>
 <vfu2ht$29m4j$1@dont-email.me> <vfu4m8$2a4tk$1@dont-email.me>
 <vfverd$9264$3@solani.org> <vfvf5g$2k94n$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 08:41:10 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="297156"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:vN+sYWKnzIFIhwV9sLCxvQkFtuk=
X-User-ID: eJwFwYcRwEAIA7CV8hhTxqEc+48QibBn42o05fGiW8CtjZl3fQAC2RWZy7aCk4P9HFI79m51Vry8J0W1f2zvFiA=
Content-Language: en-US
In-Reply-To: <vfvf5g$2k94n$1@dont-email.me>
Bytes: 3059
Lines: 32

On 31.10.2024 09:29, FromTheRafters wrote:
> WM submitted this idea :
>> On 30.10.2024 21:24, FromTheRafters wrote:
>>> WM explained :
>>>> On 30.10.2024 16:43, FromTheRafters wrote:
>>>>> on 10/30/2024, WM supposed :
>>>>
>>>>>> 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.
>>>>>
>>>>> Wrong.
>>>>
>>>> What? ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ?
>>>
>>> No, the other part. Your 'conclusion' is a non sequitur.
>>
>> My conclusion is that all unit fractions are separated by large sets 
>> of real points from each other. Never two or more unit fractions are 
>> at the same point. Is that what you doubt? Hardly.
>>
>> Then you must doubt that NUF(x) can grow only by 1 at any point x? But 
>> why?
> 
> Because NUF() doesn't "grow" it just *is*.

According to set theory every function just "is". But we analyze or 
describe its behaviour with increasing argument x as increasing, 
constant or decreasing. Should that be forbidden in case of NUF in order 
to avoid problems?

Regards, WM