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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 22 Dec 2024 20:03:21 -0500
Organization: i2pn2 (i2pn.org)
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On 12/22/24 10:04 AM, WM wrote:
> On 22.12.2024 13:28, Richard Damon wrote:
>> On 12/21/24 4:40 PM, WM wrote:
> 
>>> The reason is that after every visible unit fraction there are more 
>>> visible unit fractions created. That is potential infinity. You can't 
>>> understand that matter.
>>
>> No, they are not "created" they have always been there, they just 
>> haven't been enumerated/discovered yet.
> 
> Why haven't they?

Because you just haven't had time to discover it, because you are a 
finite entity.

A finite universe can only describe a finite number of finite number, 
but the mathematical set of the natural numbers goes beyond that.

>>>> The numbers didn't just show up, they were always there and we 
>>>> didn't do anything that prohibited it from stopping at any of them.
>>>
>>> They were dark.
>>
>> No, you just didn't see them because your logic closes its eyes and 
>> lies to you.
> 
> Then show me a unit fraction that you see for the first time when going 
> from 0 to 1 which has no smaller unit fractions that you hadn't 
> discovered before.
> 

But the question isn't "hadn't discovered befor" but which exists. An 
there isn't a "first" unit fraction on the line from that end, because 
the set is unbounded, so asking about where something that doesn't exist 
would be is just an invalid question.





> Regards, WM
>