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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sat, 12 Oct 2024 16:07:44 -0400
Organization: Peripheral Visions
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WM used his keyboard to write :
> 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.

Wrong, you disbelieve (when it suits you) the idea of cardinality. How 
is that 'using the properties'?