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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 10:30:42 +0200
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On 15.10.2024 00:27, Chris M. Thomasson wrote:

> Take the index, using natural numbers
> 
> 1: { 1 }
> 2: { 1, 2 }
> 3: { 1, 2, 3 }
> 4: { 1, 2, 3, 4 }
> ...
> 
> vs:
> 
> 1: { 2 }
> 2: { 2, 4 }
> 3: { 2, 4, 6 }
> 4: { 2, 4, 6, 8 }
> ...
> 
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