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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: Thu, 24 Oct 2024 12:46:10 -0700
Organization: A noiseless patient Spider
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On 10/24/2024 11:58 AM, WM wrote:
> 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.

{ 1, 2, 3, 4, ... }

{ 1*2, 2*2, 3*2, 4*2, ... }

{ (1*2)/2, (2*2)/2, (3*2)/2, (4*2)/2, ... }

Nothing is lost at all! WTF are you rambling on about! ???