Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Wed, 1 Jan 2025 13:51:02 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <4d797c9134ea480aa4976cf866cacaede8d309bd@i2pn2.org>
References: <vg7cp8$9jka$1@dont-email.me> <vk23m7$31l8v$1@dont-email.me>
	<bce1b27d-170c-4385-8938-36805c983c49@att.net> <vk693m$f52$2@dont-email.me>
	<a17eb8b6-7d11-4c59-b98c-b4d5de8358ca@att.net> <vk7dmb$7mh2$2@dont-email.me>
	<b72490c1-e61a-4c23-a3a5-f624b2c084e4@att.net> <vk8tbq$j9h1$1@dont-email.me>
	<bd7dfdc7-6471-4fe6-b078-0ca739031580@att.net>
	<vklumc$3htmt$1@dont-email.me>
	<c03cf79d-0572-4b19-ad92-a0d12df53db9@att.net>
	<n9CdnR02SsevtPL6nZ2dnZfqnPidnZ2d@giganews.com>
	<45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <vkpa98$dofu$2@dont-email.me>
	<3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org>
	<vkr8sq$t59a$2@dont-email.me>
	<d4669f26483b01c8a43dfd3ac4b61ab4a42bf551@i2pn2.org>
	<vksikk$17fjt$1@dont-email.me>
	<aa2941e93e806f1dda55d563dd062db67eb879f1@i2pn2.org>
	<vktmi3$1ia1u$1@dont-email.me>
	<c46775b30460bc564b3fe7bd1b838713829024f8@i2pn2.org>
	<vkv3t1$1qb93$1@dont-email.me>
	<2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org>
	<vl1bp4$2bcos$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 1 Jan 2025 13:51:02 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="1488336"; 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: 3482
Lines: 34

Am Tue, 31 Dec 2024 19:05:24 +0100 schrieb WM:
> On 31.12.2024 16:37, Richard Damon wrote:
>> On 12/30/24 4:38 PM, WM wrote:
>>> On 30.12.2024 17:08, Richard Damon wrote:
>>>> On 12/30/24 3:44 AM, WM wrote:
>>>>> On 30.12.2024 01:36, Richard Damon wrote:
>>>>>> On 12/29/24 5:31 PM, WM wrote:
>>>>>
>>>>>>> My theorem: Every union of FISONs which stay below a certain
>>>>>>> threshold stays below that threshold.
>>>>>>> Find a counterexample. Don't claim it but prove it. Fail.
>>>>>> But what does that prove?
>>>>> That proves the existence of dark numbers.
>>>> How?
>>>> It shows that there are numbers you didn't look at, but you admit to
>>>> not looking at all the numbers.
>>> Neither can you look at more numbers.
>> Of course I can look at "more" numbers, as I can look at the one after
>> where you stopped.
> I don't stop but know that every FISON is finite as its name says and
> covers at most 1 % of ℕ.
Yes, you stop at some finite threshold.

>>>>> If ℕ is an actually infinite set then it is not made by FISONs.
>> But there is no Natural Number that isn't in a FISON, which is NOT what
>> you have been saying.
> You cannot find a natural number that isn't in a FISON. But there must
> be more because FISONs cover less than 1 % of ℕ.
No??? There are infinitely many of them, and together they form N.

>> The problem is your logic can't have "Every" FISON, because "every
>> FISON" is an infinite set of them,
-- 
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.