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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 10:17:33 +0200
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On 16.10.2024 04:45, Richard Damon wrote:
> On 10/14/24 12:37 PM, WM wrote:

>> That doubling _all_ natural numbers only yields _all_ natural numbers 
>> is impossible.

> OF course it is impossible, it only yield half of the numbers, as no odd 
> numbers are in the set.

There is a general truth: 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