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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Thu, 11 Jul 2024 14:40:56 +0200
Organization: A noiseless patient Spider
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Am 11.07.2024 um 12:34 schrieb FromTheRafters:
> Ben Bacarisse was thinking very hard :
>> Moebius <invalid@example.invalid> writes:
>>
>>> Am 11.07.2024 um 02:28 schrieb Chris M. Thomasson:
>>>> On 7/10/2024 5:24 PM, Moebius wrote:
>>>>> Am 11.07.2024 um 02:16 schrieb Chris M. Thomasson:
>>>>>
>>>>>> {a, b, c} vs { 3, 4, 5 }
>>>>>>
>>>>>> Both have the same number of elements, [...]
>>>>>
>>>>> HOW do you know that? Please define (for any sets A, B):
>>>>>
>>>>>      A and B /have the same number of elements/ iff 
>>>>> ___________________ .
>>>>>
>>>>> (i.e. fill out the blanks). :-)
>>>>>
>>>>> Hint: That's what Ben Bacarisse is asking for.
>>>>>
>>>>> Sure, it's "obvious" for us. But how would you define "have the same
>>>>> number of elements" (in mathematical terms) such that it can be 
>>>>> DEDUCED
>>>>> (!) für certain sets A and B?
>>>>>
>>>>> ________________________________________
>>>>>
>>>>> Ok, I'm slighty vicious now... :-)
>>>>>
>>>>> If a = b = c, {a, b, c} still has "the same number of elements" as {3,
>>>>> 4, 5 }? :-P

>>>> I see {a, b, c} and {3, 4, 5} and think three elements.
>>>
>>> Even if a = b = c?
>>>
>>> C'mon man! :-P
>>
>> Please, that's a red herring, and you know it!  No where did I say that
>> a, b and c stood for anything (i.e. that they might be variables in the
>> maths sense).  I this sort of context they are just distinct symbols.
> 
> Indeed!

Nonsense. (See below.)

> I sometimes try to steer WM away from 'math' symbols in sets 
> like asking for a bijection of something like {elephant, rhinoceros, 
> dune buggy} and {circle, square, megaphone}. 

Here you used well estabished /names/ (constants) for certain objects 
which - as is well known - are not identical. With other words,

elephant =/= rhinoceros
elephant =/= dune buggy
rhinoceros =/= dune buggy,

etc.

Just using DIFFERENT (but arbitrary) symbols, say "a", "b", "c", does 
not ensure for that (i.e. a =/= b, a =/= c, b =/= c).

Actually, even a = b = c is POSSIBLE in this case. (Leading to card({a, 
b, c}) = 1.)

Now consider the two (different) names ("symbols") "turtle", "chelonian".

Does {turtle, chelonian} contain 2 elements, huh?!