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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: Wed, 16 Oct 2024 10:33:52 +0200
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On 14.10.2024 17:53, joes wrote:
> Am Mon, 14 Oct 2024 15:34:59 +0200 schrieb WM:
>> On 14.10.2024 14:00, joes wrote:
>>> Am Mon, 14 Oct 2024 12:35:56 +0200 schrieb WM:
>>
>>>> False. n*2 > n for all numbers, even for infinite numbers.
>>> Of course, and if the infinity is actual, they must already be in
>>> there.
>> They cannot be there because doubling all elements of a set of naturals
>> doubles the space covered on the number line.
> It does not. Changing the elements does not change their number.
> 
There is a general rule not open to further discussion:
When doubling natural numbers we obtain natural numbers which have not 
been doubled.
In potential infinity we obtain more even natural numbers than have been 
doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.

Regards, WM