Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 7 Jan 2025 13:51:52 +0100
Organization: A noiseless patient Spider
Lines: 43
Message-ID: <vlj817$26l6t$2@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <c03cf79d-0572-4b19-ad92-a0d12df53db9@att.net> <vkp0fv$b7ki$2@dont-email.me>
 <b125beff-cb76-4e5a-b8b8-e4c57ff468e9@att.net> <vkr8j0$t59a$1@dont-email.me>
 <98519289-0542-40ce-886e-b50b401ef8cf@att.net> <vksicn$16oaq$7@dont-email.me>
 <8e95dfce-05e7-4d31-b8f0-43bede36dc9b@att.net> <vl1ckt$2b4hr$1@dont-email.me>
 <53d93728-3442-4198-be92-5c9abe8a0a72@att.net> <vl5tds$39tut$1@dont-email.me>
 <9c18a839-9ab4-4778-84f2-481c77444254@att.net> <vl87n4$3qnct$1@dont-email.me>
 <8ef20494f573dc131234363177017bf9d6b647ee@i2pn2.org>
 <vl95ks$3vk27$2@dont-email.me> <vl9ldf$3796$1@dont-email.me>
 <vlaskd$cr0l$2@dont-email.me> <vlc68u$k8so$1@dont-email.me>
 <vldpj7$vlah$7@dont-email.me>
 <a8b010b748782966268688a38b58fe1a9b4cc087@i2pn2.org>
 <vlei6e$14nve$1@dont-email.me> <66868399-5c4b-4816-9a0c-369aaa824553@att.net>
 <4iKdnULFG5CGGOH6nZ2dnZfqnPqdnZ2d@giganews.com>
 <vliv5n$256n9$1@dont-email.me>
 <7dc0b7de7ad8424ac6efb0666cead929998b8d67@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 07 Jan 2025 13:51:51 +0100 (CET)
Injection-Info: dont-email.me; posting-host="ae605ac3e7bf74a89532ac4e88c94750";
	logging-data="2315485"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+5WYWpTOy1uWcS5vj7CJ2S71Fr6Z0kQyo="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:/WCfyXdGR1BoSF6CpehZMkg9wBc=
In-Reply-To: <7dc0b7de7ad8424ac6efb0666cead929998b8d67@i2pn2.org>
Content-Language: en-US
Bytes: 3346

On 07.01.2025 13:35, Richard Damon wrote:
> On 1/7/25 5:20 AM, WM wrote:
>> On 07.01.2025 02:36, Ross Finlayson wrote:
>>> On 01/06/2025 02:43 PM, Jim Burns wrote:
>>
>>>> It would be great if you (WM) did NOT
>>>> find lemma 1 weird,
>>>> but it is what it is.
>>
>> It is not weird. But your conclusions are weird.
>>
>>> The inductive set being covered by
>>> initial segments is an _axiom_ of ZF.
>>
>> And the existence of the set ℕ is also an axiom of ZF. Therefore ZF is 
>> incompatible with mathematics.
> 
> No, ZF doesn't have as an axiom that the set of Natural Numbers exist.

AoI: There exists an infinite set S.
>> All FISONs stay below the threshold |ℕ|/100, or in other words, 
>> multiplication of any FISON by 100 is insufficient to cover |ℕ|.
>>
> 
> So? The union of an infinite set of them can have properites different 
> that any set that is a union of only a finite number of them. That is a 
> nature of infinity.

It is the nature of fools to believe every nonsense.
> 
>> Every union of FISONs {1, 2, 3, ..., n} which stay below this 
>> threshold stays below this threshold too.
> 
> But not the union of *EVERY* FISON, the FULL INFINITE set of them. 

All are below 1 %.

> SOething your "logic" can't handle,

Luckily.

Regards, WM