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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Sat, 5 Apr 2025 22:51:32 +0200
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On 05.04.2025 21:08, FromTheRafters wrote:
> WM was thinking very hard :
>> On 04.04.2025 23:12, FromTheRafters wrote:
>>> WM wrote on 4/4/2025 :
>>
>>>> You are caught in a world of stupidity. Set theorists have damaged 
>>>> the honour of human intellect even more than Pope Pius XII.
>>>>
>>>> When an element is added to a set, then this set is no longer the 
>>>> same but different because the number of its members is different.
>>>
>>> How do you know that they are not 'the same'?
>>
>> A set containing element x is not the same as a set not containing 
>> element x.
> 
> Then of course they are not "the same" but are they equivalent in size?

According to Cantor they are equivalent or have same cardinality. But 
that is not a useful notion *because* sets with different number of 
members are called equivalent.

Regards, WM