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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 15 Oct 2024 22:45:08 -0400
Organization: i2pn2 (i2pn.org)
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On 10/14/24 9:40 AM, WM wrote:
> On 14.10.2024 14:15, joes wrote:
> 
>> No, we are taking the complete, actually infinite set which reaches
>> to "before" w.
> 
> and fills the space between 0 and ω evenly. Same happens with the 
> doubled set between 0 and ω2.
> 
> Regards, WM
> 

Nope, because omega wasn't in the first set, so since every element in 
the doubled set is also in the undoubled set, the ordinal "after" the 
set is still that original omega.

The problem is you seem to imagine the actual infinity as if it was 
finite and had a end, which it doesn't have.

If you can't imagine an actually created infinte set of numbers without 
an end, you can't imagine an actually created infinite set, since that 
is one of its properties.