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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 16 Oct 2024 10:55:10 -0700
Organization: A noiseless patient Spider
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On 10/16/2024 1:17 AM, WM wrote:
> 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.

Did you ride the _really_ short bus to school?