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? (infinitary)
Date: Sat, 12 Oct 2024 22:50:25 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <54699971b4dc5e672bdee847482d377a03144531@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org>
	<4bc3b086-247a-4547-89cc-1d47f502659d@tha.de> <ve0n4i$1vps$1@news.muc.de>
	<ve10qb$1p7ge$1@dont-email.me> <ve117p$vob$1@news.muc.de>
	<ve315q$24f8f$3@dont-email.me> <ve46vu$324$2@news.muc.de>
	<ve5u2i$2jobg$4@dont-email.me> <ve6329$19d5$1@news.muc.de>
	<ve64kl$2m0nm$4@dont-email.me> <ve66f3$19d5$2@news.muc.de>
	<ve683o$6c2o$1@solani.org> <ve6a23$19d5$3@news.muc.de>
	<ve6c3b$6esq$2@solani.org> <ve6kl1$207d$1@news.muc.de>
	<ve96jj$38qui$2@dont-email.me> <ve97c7$2f64$1@news.muc.de>
	<ve97qj$38qui$4@dont-email.me>
	<3f5fcf13171337f1c3d2ef84cc149be327648451@i2pn2.org>
	<veecr3$7rap$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 12 Oct 2024 22:50:25 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="1680996"; 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: 3457
Lines: 36

Am Sat, 12 Oct 2024 19:49:23 +0200 schrieb WM:
> On 10.10.2024 21:54, joes wrote:
>> Am Thu, 10 Oct 2024 20:53:07 +0200 schrieb WM:
>>> On 10.10.2024 20:45, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>
>>>>> If all natnumbers are there and if 2n is greater than n, then the
>>>>> doubled numbers do not fit into ℕ.
>>>> For any finite n greater than zero, 2n is greater than n.  The same
>>>> does not hold for infinite n.
>>> There are no infinite n = natural numbers.
>> Exactly! There are furthermore no infinite doubles of naturals (2n).
> But the doubles are larger. Hence after doubling the set has a smaller
> density and therefore a larger extension on the real line. Hence not all
> natural numbers have been doubled.
Taking "density" here to mean cardinality div. by size(?) makes it pretty
much undefined, since those are both infinite - with N just as with 2N=G
(what's the difference anyway?). The real line reaches until, but does not
include omega, no matter your step size. What value do you suppose n^2
and n^n diverge to?

>>>>>>> Numbers multiplied by 2 do not remain unchanged.
>>>>> Either doubling creates new natural numbers. Then not all have been
>>>>> doubled. Or all have been doubled, then some products fall outside
>>>>> of ℕ.
>>>> No.  Not even close.
>>> Deplorable. But note that all natural numbers are finite and follow
>>> this law: When doubled then 2n > n. If a set of natural numbers is
>>> doubled, then the results cover a larger set than before..
>> Additionally: if n is finite, so is 2n. It cannot go beyond w.
> Then there is no complete set. The doubling can be repeated and
> repeated. Always new numbers are created. Potential infinity.
No! Actual infinity already includes all doubles of all numbers.

-- 
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.