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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 12 Oct 2024 10:55:46 -0400
Organization: i2pn2 (i2pn.org)
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On 10/12/24 9:32 AM, WM wrote:
> On 10.10.2024 21:48, joes wrote:
>> Am Wed, 09 Oct 2024 18:47:39 +0200 schrieb WM:
> 
>>> Numbers multiplied by 2 do not remain unchanged. That is not intuition
>>> but mathematics.
>> They do, however, remain natural.
> 
> They do not remain the same set as before. They cover more of the real 
> line. If they all are natnumbers, then there are more than at the 
> outset. That means potential infinity. If there are not more natumbers 
> than at the outset, then infinite numbers have been created. There is no 
> way to avoid one of these results.
> 
> Regards, WM
> 

No, they do not cover "more" of the line, as they still cover exactly 
Aleph_0 point within the range of the finite numbers below omega.

The problem is you are applying properties of FINITE sets to an infinite 
set, which just doen't apply. The problem is that you think of 
"infinite" as just some really big and huge number, but it is something 
different.

The infinite set, when completed, doesn't HAVE an "end" at the top, but 
goes on and on and on without end. We can thing of that going on 
incrementally in a way we can understand, giving us that "potential 
infinity" which you talk about (but that potential, when fully developed 
is infinite), or we can try to imagine the process being completed, but 
then it is something we have NEVER actually experienced, and has 
properties we don't understand, so we can't actually "perceive" what it is.

YOU imagine an end to it, which it doesn't have, infinite, by its 
definition, has no end, so you make an error by assuming it.

The problem is you are just stuck in your finite thinking, and can't 
understand the basics of what infinity is like. Others, because they are 
willing to learn by looking at the potential, understand a bit about the 
infinite, even if we can not fully understand it (since it is bigger 
than what we can know).

Sorry, you are just showing the complete finite boundness of your logic.