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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
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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?
[...]