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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Contradiction of bijections as a measure for infinite sets
Date: Fri, 05 Apr 2024 08:57:27 -0400
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WM explained on 4/4/2024 :
> Le 03/04/2024 à 15:59, FromTheRafters a écrit :
>> WM presented the following explanation :
>>> Le 02/04/2024 à 17:51, Jim Burns a écrit :
>>>> On 4/2/2024 3:36 AM, WM wrote:
>>>
>>>> If your assumption leads to "no bijection",
>>>> but there is a bijection,
>>>> then your assumption is wrong.
>>>
>>> My trick proves that there is no bijection.
>>> Or could you explain why first bijecting n and n/1 should destroy an 
>>> existing bijection?
>> 
>> Your 'trick' only fails to demonstrate a bijection. Failing to demonstrate 
>> a bijection does not mean that there is no bijection, only that your 
>> 'trick' doesn't work to that end.
>
> Explain why first bijecting n and n/1 should destroy an existing bijection!

You still seem to think that sets change. If you mean 'n' is an element 
of the naturals then of course N bijects with the naturals as embedded 
in Q. Also, the complement of the naturals over one in Q is the same 
size as the proper subset you created. No sets (read also functions) 
were destroyed.