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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: Fri, 17 Jan 2025 09:52:32 -0500
Organization: i2pn2 (i2pn.org)
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On 1/17/25 5:50 AM, WM wrote:
> On 17.01.2025 01:37, Richard Damon wrote:
>> On 1/16/25 10:19 AM, WM wrote:
>>> On 16.01.2025 13:27, Richard Damon wrote:
>>>
>>>> The potential infinity itself isn't growing, our KNOWLEDGE of it 
>>>> grows as we generate its members.
>>>
>>> But the knowledge of actually infinite sets isn't growing?
> 
>> Depends how good you can think.
> 
> No, it has nothing to do with your missing knowledge or your lack of 
> thinking capability. "Potential infinity refers to a procedure that gets 
> closer and closer to, but never quite reaches, an infinite end. [...] 
> Completed infinity, or actual infinity, is an infinity that one actually 
> reaches; the process is already done."[E. Schechter: "Potential versus 
> completed infinity: Its history and controversy" (5 Dec 2009)]
> 
> Regards, WM
> 

That "definition" violates to definition that set don't change.

What gets closer and closer is our KNOWLEDGE of the fixed and complete set.

Since we can only do "logic" on "knowledge".

Yes, there are different ways to describe this, but if you want to use 
the logic of fixed sets, potential infinity is potential for knowledge.

Some may talk of a growing set, but then you can't use any logic based 
on "fixed" sets.

IT seems your naive logic doesn't understand that basic concept, and 
tries to mix statements ignoring the context of them.