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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, 19 Oct 2024 11:24:54 +0200
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On 18.10.2024 03:26, Richard Damon wrote:
> On 10/17/24 2:46 PM, WM wrote:
>> On 17.10.2024 02:18, Richard Damon wrote:
>>> On 10/16/24 1:18 PM, WM wrote:
>>
>>>> Of course it is a general rule. Doubling creates larger numbers.
>>
>>> But those numbers are still in the set, and all the members of the 
>>> set were doubled, so none of the doubled values got us to a value 
>>> that wasn't doubled.
>>
>> Therefore not all doubles are natural.

> So, what ones aren't?

They all are dark and cannot be named individually.
> 
> It is proven that the set of Natural Numbers are closed under 
> multiplication.

That is not the set but the potentially infinite collection of Peano 
numbers.
> 
Regards, WM