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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 12 Oct 2024 17:10:41 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 12 Oct 2024 15:32:25 +0200 schrieb WM:
> 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.
Of course multiplying a (finite) number by 2 changes the value.
If anything, the even numbers cover less, being a subset of the naturals.
If doubling a natural yielded omega, there would need to be an n = w/2.
That is not defined, nor finite.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.