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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: Sun, 20 Oct 2024 21:34:38 +0200
Organization: A noiseless patient Spider
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On 20.10.2024 20:50, Jim Burns wrote:
> On 10/20/2024 3:40 AM, WM wrote:
>> 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.
> 
> It is my claim that
> infinitely.many exchanges in an infinite set
> can result in the loss of one of them.
> 1 is not infinite.

Every exchange is one and has to obey logic.

If your claim was acceptable, then every enumeration of an infinite set 
could lose elements. Therefore it is rejected as detrimental to set theory.

>> 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.
> 
> A finite set can be ordered such that
> each subset holds its top and bottom or is empty.

If it did not contain dark elements and in spite of that was complete, 
the same could be done there.

Regards, WM