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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
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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?