Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 2 Dec 2024 21:34:05 -0800
Organization: A noiseless patient Spider
Lines: 45
Message-ID: <vim58c$3sjje$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <4a810760-86a1-44bb-a191-28f70e0b361b@att.net> <vi6uc3$3v0dn$4@dont-email.me>
 <b2d7ee1f-33ab-44b6-ac90-558ac2f768a7@att.net> <vi7tnf$4oqa$1@dont-email.me>
 <23311c1a-1487-4ee4-a822-cd965bd024a0@att.net>
 <e9eb6455-ed0e-43f6-9a53-61aa3757d22d@tha.de>
 <71758f338eb239b7419418f49dfd8177c59d778b@i2pn2.org>
 <via83s$jk72$2@dont-email.me> <viag8h$lvep$1@dont-email.me>
 <viaj9q$l91n$1@dont-email.me> <vibvfo$10t7o$1@dont-email.me>
 <vic6m9$11mrq$4@dont-email.me> <vicbp2$1316h$1@dont-email.me>
 <vid4ts$1777k$2@dont-email.me> <vidcv3$18pdu$1@dont-email.me>
 <bdbc0e3d-1db2-4d6a-9f71-368d36d96b40@tha.de> <vier32$1madr$1@dont-email.me>
 <vierv5$1l1ot$2@dont-email.me> <viiqfd$2qq41$5@dont-email.me>
 <vijhrd$34mp8$1@dont-email.me> <vilh59$3k21l$5@dont-email.me>
 <vilheq$3ks01$3@dont-email.me> <vilhjk$3k21l$9@dont-email.me>
 <vilhk8$3ks01$4@dont-email.me> <vilhnl$3k21l$10@dont-email.me>
 <viljdo$3k21l$12@dont-email.me> <vim52i$3s6qb$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 03 Dec 2024 06:34:05 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f777e730b2e8168ebcdb2932c05660c1";
	logging-data="4083310"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+Mj4WRyYQ3Q769zzHTtc3DFRhVavTZA38="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:BY6nu0qsx6RHqcLKvyMUt5uzbvg=
In-Reply-To: <vim52i$3s6qb$1@dont-email.me>
Content-Language: en-US
Bytes: 3236

On 12/2/2024 9:30 PM, Moebius wrote:
> Am 03.12.2024 um 01:29 schrieb Chris M. Thomasson:
>> On 12/2/2024 4:00 PM, Chris M. Thomasson wrote:
>>> On 12/2/2024 3:59 PM, Moebius wrote:
>>>> Am 03.12.2024 um 00:58 schrieb Chris M. Thomasson:
>>>>> On 12/2/2024 3:56 PM, Moebius wrote:
>>>>>> Am 03.12.2024 um 00:51 schrieb Chris M. Thomasson:
>>>>>>> On 12/1/2024 9:50 PM, Moebius wrote:
>>>>>>>> Am 02.12.2024 um 00:11 schrieb Chris M. Thomasson:
>>>>>>>>> On 11/30/2024 3:12 AM, WM wrote:
>>>>>>>>
>>>>>>>>>> Finite initial segment[s]: F(n) = {1, 2, 3, ..., n}    (n e IN).
>>>>>>> [...]
>>>>>>>
>>>>>>> When WM writes:
>>>>>>>
>>>>>>> {1, 2, 3, ..., n}
>>>>>>>
>>>>>>> I think he might mean that n is somehow a largest natural number?
>>>>>>
>>>>>> Nope, n here may be any element in IN.
>>>>>
>>>>> So if n = 5, the FISON is:
>>>>>
>>>>> { 1, 2, 3, 4, 5 }
>>>>>
>>>>> [If} n = 3
>>>>>
>>>>> { 1, 2, 3 }
>>>>>
>>>>> Right?
>>>>
>>>> Right.
>>>
>>> Thank you Moebius. :^)
>>
>> So, if n = all_of_the_naturals, then
> 
> No, /n/ has to be a natural number, i.e. an element in IN.

Ahhhh. Okay with me.

What about {1, 2, 3, ..., n}, where n is taken to infinity? No limit?

[...]