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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: Thu, 24 Oct 2024 20:58:45 +0200
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On 24.10.2024 19:34, Jim Burns wrote:
> On 10/24/2024 6:58 AM, WM wrote:

>> All that is accepted and doubled.
> 
> The subset of those with a double not.in ℕ
> holds no minimum.

The whole set with all its numbers exists and can be mapped to the 
double numbers. That halves the density and doubles the covered interval.
> After all swaps,
> Bob is not in any room he was ever in.
> 'Bye, Bob.

After all swaps Bob is in a room, because there is nowhere an outlet.
> 
> Note well:
> After all _infinitely many_ swaps,
> Bob is not in any of _infinitely many_ rooms he was ever in.
> 
> Infinite is different from finite.

Bobs cannot dissolve into nothing. If you despise logic, why do you 
maintain it with Cantor's procedures? If Bobs can disappear also other 
numbers can disappear.

> The problem with Bob disappearing is that
> Bob disappearing is not a problem.
> It's not repairable because it's not broken.

Lossless exchanges remain lossless forever. But I can understand that 
you have to apply Freudian repression. Eyes wide shut.

Regards, WM