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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 12 Oct 2024 20:50:34 +0200
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On 12.10.2024 16:55, Richard Damon wrote:
> 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.

> 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.

Wrong.
> 
> The problem is you are applying properties of FINITE sets

Wrong, I use properties of finite numbers.

Regards, WM