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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]
Date: Fri, 04 Apr 2025 17:12:27 -0400
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WM wrote on 4/4/2025 :
> On 04.04.2025 18:41, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 03.04.2025 21:10, Alan Mackenzie wrote:
>> 
>>>>> It is not at all difficult to understand. Difficult to understand is
>>>>> only why cardinality is used at all.
>> 
>>>> Those two sentences contradict eachother.  Cardinality is used because it
>>>> is a sensible way of comparing the size of sets.
>> 
>>> No.
>> 
>> You're wrong.
>
> 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'? No bijection perhaps?