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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sun, 20 Oct 2024 07:20:29 -0400
Organization: Peripheral Visions
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References: <vb4rde$22fb4$2@solani.org>   <veirkn$desj$2@solani.org> <db221d267ae4b956cd0818c9b5ccc0311df97d1e@i2pn2.org> <60f1280e-e226-4314-8eca-da5410be8ca3@tha.de> <96a7aa944085e76faed69c8db9a8dca599e1a159@i2pn2.org> <vejhcb$ditg$1@solani.org> <2c732eefb860986209bd46ed88391ddceaddff55@i2pn2.org> <vOmcnYVG-OHpKZP6nZ2dnZfqnPSdnZ2d@giganews.com> <avecnXK3J6VsU5P6nZ2dnZfqnPhg4p2d@giganews.com> <vensvb$2533b$2@dont-email.me> <veoumv$2bc1q$4@dont-email.me> <veovbm$2bc2g$2@dont-email.me> <aqCcnTFQ7MNz_436nZ2dnZfqnPudnZ2d@giganews.com> <bd2fe5d4-c284-47e7-a265-720539d2ab42@att.net> <27WcnWnC9tjPyIz6nZ2dnZfqn_idnZ2d@giganews.com> <f1e485be-dc79-49ba-87fa-4bb23910d878@att.net> <4d080bc4-7c84-4951-a8f4-9bf0f95ad47f@tha.de> <dcd6560e-e5cc-4c14-8607-c32977f6c622@att.net> <vf042r$3rmh1$1@dont-email.me> <c3993c0d-1904-4b7e-ae45-cf2651cc5eb0@att.net> <vf0tno$6c6$1@dont-email.me> <2f1438e0-4b73-474c-afe6-f8dcb1b71743@att.net> <vf2c55$ambv$2@dont-email.me>
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WM was thinking very hard :
> On 20.10.2024 00:08, Jim Burns wrote:
>> On 10/19/2024 2:28 PM, WM wrote:
>
>>>
>>> The contradiction is independent of infinity.
>>> It is your claim that
>> 
>> infinitely.many exchanges in an infinite set
>> (vanishing Bob)
>
> Every exchange is _one_ lossless exchange.
>> 
>>> exchanging two objects
>>> can result in the loss of one of them.
>> 
>> I fixed that for you.
>
> It is nonsense like:
> ∀n ∈ ℕ: |{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2
> but |{2, 4, 6, ...}|/|{1, 2, 3, 4, 5, 6, ...} = 1.

You made some typos here. You left out a couple of "|" for the 
cardinalities.

Plus, how do you define division on cardinalities -- especially the 
infinite ones?