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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Thu, 11 Jul 2024 06:34:59 -0400
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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 = 1?
>> 
>> 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! 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}. Bijections work for any 
sets, not just numerical ones -- easier to demonstrate with numbers 
though because you can use set builder notation instead of just roster 
form for really large 'number cumbersome' sets.