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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sat, 7 Dec 2024 17:30:13 -0500
Organization: i2pn2 (i2pn.org)
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On 12/7/24 4:31 PM, Chris M. Thomasson wrote:
> On 12/7/2024 4:20 AM, Richard Damon wrote:
>> On 12/7/24 5:44 AM, WM wrote:
>>> On 06.12.2024 14:30, joes wrote:
>>>> Am Thu, 05 Dec 2024 17:04:58 +0100 schrieb WM:
>>>>> On 05.12.2024 13:56, joes wrote:
>>>>>> Am Thu, 05 Dec 2024 12:42:17 +0100 schrieb WM:
>>>>>
>>>>>>> But every number you can take belongs to a vanishing subset of ℕ.
>>>>>> What does that have to do with the ability to be "chosen"?
>>>>> It is impossible to choose a number outside of a tiny subset.
>>>> Duh. There are no other numbers.
>>>
>>> May be. My statements however concern completed infinity. The subset 
>>> is never complete.
>>>
>>> Regards, WM
>>>
>>
>> And thus the limit of the subsets is not complete either, per your 
>> logic of a limit of constants is always that same constant. Thus, your 
>> trying to define the complete infinity just fails.
> 
> WM seems to think that "completed" means there simply must be a largest 
> natural number? I can only guess here.

He seems to think that Completed means all of them, but then he assumes 
that if you have "all" of a set, that set must have a last element.

This comes from the fact that the only sets he can have are finite, and 
complete finite sets have a last element.

He just doesn't get that a complete infinite set doesn't necessarily 
have a "last" element in it, because that concept is just unimaginable 
to his tiny brain.