Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 7 Oct 2024 15:10:55 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <9402bbc384ade20d6fafc9ff0534e7c6f5ae4581@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <vdpbuv$alvo$1@dont-email.me>
	<8c94a117d7ddaba3e7858116dc5bc7c66a46c405@i2pn2.org>
	<vdqttc$mnhd$1@dont-email.me> <vdr1g3$n3li$6@dont-email.me>
	<8ce3fac3a0c92d85c72fec966d424548baebe5af@i2pn2.org>
	<vdrd5q$sn2$2@news.muc.de>
	<55cbb075e2f793e3c52f55af73c82c61d2ce8d44@i2pn2.org>
	<vdrgka$sn2$3@news.muc.de> <vds38v$1ih6$6@solani.org>
	<vdscnj$235p$1@news.muc.de> <vdtt15$16hg6$4@dont-email.me>
	<vdu54i$271t$1@news.muc.de> <vduata$19d4m$1@dont-email.me>
	<vduf0m$1tif$1@news.muc.de> <ve076s$1kopi$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 7 Oct 2024 15:10:55 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="952087"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM";
User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a
 git.gnome.org/pan2)
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 3631
Lines: 43

Am Mon, 07 Oct 2024 10:47:25 +0200 schrieb WM:
> On 06.10.2024 18:48, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 06.10.2024 15:59, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>> 
>>>>> All unit fractions are separate points on the positive real axis,
>>>>> but there are infinitely many for every x > 0.
>>>>> That can only hold for definable x, not for all.
>>>> Poppycock!  You'll have to do better than that to provide such a
>>>> contradiction.
>>> It is good enough, but you can't understand.
>> I do understand.  I understand that what you are writing is not maths.
>> I'm trying to explain to you why.  I've already proved that there are
>> no "undefinable" natural numbers.  So assertions about them can not
>> make any sense.
> You have not understood that all unit fractions are separate points on
> the positive axis. Every point is a singleton set and could be seen as
> such, but it cannot. Hence it is dark.
Why can some points not be „seen” as a singleton set? 

>>>>   Hint: Skilled mathematicians have worked on trying to
>>>> prove the inconsistency of maths, without success.
>>> What shall that prove? Try to understand.
>> It shows that any such results are vanishingly unlikely to be found by
>> non-specialists such as you and I.
> Unlikely is not impossible.
Nothing is impossible…

>>> Try only to understand my argument. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. How can
>>> infinitely many unit fractions appear before every x > 0?
>> You are getting confused with quantifiers, here.  For each such x,
>> there is an infinite set of fractions less than x.  For different x's
>> that set varies.  There is no such infinite set which appears before
>> every x > 0.
> The set varies but infinitely many elements remain the same. A shrinking
> infinite set which remains infinite has an infinite core.
Here is your essential misunderstanding: there is no mysterious Something
that makes a set infinite. It is infinite because it is not finite, has
no natural number as its size.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.